import java.io.*;
import java.util.*;
 
 
public class Main{
   public static void main(String[] args) {
      MyScanner sc = new MyScanner();
      out = new PrintWriter(new BufferedOutputStream(System.out));
      
      // Start writing your solution here. -------------------------------------
   int k = sc.nextInt();
     int n = sc.nextInt();
     int [] a = new int[n];
     for(int i = 0; i < n ; i ++)
       a[i] = sc.nextInt();
     int max = a[0] + k - a[n - 1];
     for(int i = 1; i < n ; i ++)
       max = Math.max(max, a[i] - a[i - 1]);
     out.println(k - max);
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */

      // Stop writing your solution here. -------------------------------------
      out.close();
   }

     

   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   }
   //--------------------------------------------------------
} import java.io.*; io.* java import java.util.*; util.* java public class Main{
   public static void main(String[] args) {
      MyScanner sc = new MyScanner();
      out = new PrintWriter(new BufferedOutputStream(System.out));
      
      // Start writing your solution here. -------------------------------------
   int k = sc.nextInt();
     int n = sc.nextInt();
     int [] a = new int[n];
     for(int i = 0; i < n ; i ++)
       a[i] = sc.nextInt();
     int max = a[0] + k - a[n - 1];
     for(int i = 1; i < n ; i ++)
       max = Math.max(max, a[i] - a[i - 1]);
     out.println(k - max);
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */

      // Stop writing your solution here. -------------------------------------
      out.close();
   }

     

   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   }
   //--------------------------------------------------------
} Main //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out; out public static void main(String[] args) {
      MyScanner sc = new MyScanner();
      out = new PrintWriter(new BufferedOutputStream(System.out));
      
      // Start writing your solution here. -------------------------------------
   int k = sc.nextInt();
     int n = sc.nextInt();
     int [] a = new int[n];
     for(int i = 0; i < n ; i ++)
       a[i] = sc.nextInt();
     int max = a[0] + k - a[n - 1];
     for(int i = 1; i < n ; i ++)
       max = Math.max(max, a[i] - a[i - 1]);
     out.println(k - max);
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */

      // Stop writing your solution here. -------------------------------------
      out.close();
   } main {
      MyScanner sc = new MyScanner();
      out = new PrintWriter(new BufferedOutputStream(System.out));
      
      // Start writing your solution here. -------------------------------------
   int k = sc.nextInt();
     int n = sc.nextInt();
     int [] a = new int[n];
     for(int i = 0; i < n ; i ++)
       a[i] = sc.nextInt();
     int max = a[0] + k - a[n - 1];
     for(int i = 1; i < n ; i ++)
       max = Math.max(max, a[i] - a[i - 1]);
     out.println(k - max);
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */

      // Stop writing your solution here. -------------------------------------
      out.close();
   } MyScanner sc = new MyScanner(); sc new MyScanner() out = new PrintWriter(new BufferedOutputStream(System.out)) out new PrintWriter(new BufferedOutputStream(System.out)) int k = sc.nextInt(); k sc.nextInt() sc.nextInt sc int n = sc.nextInt(); n sc.nextInt() sc.nextInt sc int [] a = new int[n]; a new int[n] n for(int i = 0; i < n ; i ++)
       a[i] = sc.nextInt(); int i = 0; int i = 0; i 0 i < n i n i ++ i ++ i a[i] = sc.nextInt(); a[i] = sc.nextInt() a[i] a i sc.nextInt() sc.nextInt sc int max = a[0] + k - a[n - 1]; max a[0] + k - a[n - 1] a[0] + k a[0] a 0 k a[n - 1] a n - 1 n 1 for(int i = 1; i < n ; i ++)
       max = Math.max(max, a[i] - a[i - 1]); int i = 1; int i = 1; i 1 i < n i n i ++ i ++ i max = Math.max(max, a[i] - a[i - 1]); max = Math.max(max, a[i] - a[i - 1]) max Math.max(max, a[i] - a[i - 1]) Math.max Math max a[i] - a[i - 1] a[i] a i a[i - 1] a i - 1 i 1 out.println(k - max) out.println out k - max k max out.close() out.close out String[] args args public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   } MyScanner BufferedReader br; br StringTokenizer st; st public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      } MyScanner {
         br = new BufferedReader(new InputStreamReader(System.in));
      } br = new BufferedReader(new InputStreamReader(System.in)) br new BufferedReader(new InputStreamReader(System.in)) String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      } next {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      } while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          } st == null || !st.hasMoreElements() st == null st null !st.hasMoreElements() st.hasMoreElements() st.hasMoreElements st {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          } try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              } catch (IOException e) {
                  e.printStackTrace();
              } IOException e {
                  e.printStackTrace();
              } e.printStackTrace() e.printStackTrace e {
                  st = new StringTokenizer(br.readLine());
              } st = new StringTokenizer(br.readLine()) st new StringTokenizer(br.readLine()) return st.nextToken(); st.nextToken() st.nextToken st int nextInt() {
          return Integer.parseInt(next());
      } nextInt {
          return Integer.parseInt(next());
      } return Integer.parseInt(next()); Integer.parseInt(next()) Integer.parseInt Integer next() next long nextLong() {
          return Long.parseLong(next());
      } nextLong {
          return Long.parseLong(next());
      } return Long.parseLong(next()); Long.parseLong(next()) Long.parseLong Long next() next double nextDouble() {
          return Double.parseDouble(next());
      } nextDouble {
          return Double.parseDouble(next());
      } return Double.parseDouble(next()); Double.parseDouble(next()) Double.parseDouble Double next() next String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      } nextLine {
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      } String str = ""; str "" try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  } catch (IOException e) {
	     e.printStackTrace();
	  } IOException e {
	     e.printStackTrace();
	  } e.printStackTrace() e.printStackTrace e {
	     str = br.readLine();
	  } str = br.readLine() str br.readLine() br.readLine br return str; str public class Main{
   public static void main(String[] args) {
      MyScanner sc = new MyScanner();
      out = new PrintWriter(new BufferedOutputStream(System.out));
      
      // Start writing your solution here. -------------------------------------
   int k = sc.nextInt();
     int n = sc.nextInt();
     int [] a = new int[n];
     for(int i = 0; i < n ; i ++)
       a[i] = sc.nextInt();
     int max = a[0] + k - a[n - 1];
     for(int i = 1; i < n ; i ++)
       max = Math.max(max, a[i] - a[i - 1]);
     out.println(k - max);
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */

      // Stop writing your solution here. -------------------------------------
      out.close();
   }

     

   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   }
   //--------------------------------------------------------
} public class Main{
   public static void main(String[] args) {
      MyScanner sc = new MyScanner();
      out = new PrintWriter(new BufferedOutputStream(System.out));
      
      // Start writing your solution here. -------------------------------------
   int k = sc.nextInt();
     int n = sc.nextInt();
     int [] a = new int[n];
     for(int i = 0; i < n ; i ++)
       a[i] = sc.nextInt();
     int max = a[0] + k - a[n - 1];
     for(int i = 1; i < n ; i ++)
       max = Math.max(max, a[i] - a[i - 1]);
     out.println(k - max);
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */

      // Stop writing your solution here. -------------------------------------
      out.close();
   }

     

   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   }
   //--------------------------------------------------------
} Main
import java.io.*;
import java.util.*;
 
 
public class Main{
   public static void main(String[] args) {
      MyScanner sc = new MyScanner();
      out = new PrintWriter(new BufferedOutputStream(System.out));
      
      // Start writing your solution here. -------------------------------------
   int k = sc.nextInt();
     int n = sc.nextInt();
     int [] a = new int[n];
     for(int i = 0; i < n ; i ++)
       a[i] = sc.nextInt();
     int max = a[0] + k - a[n - 1];
     for(int i = 1; i < n ; i ++)
       max = Math.max(max, a[i] - a[i - 1]);
     out.println(k - max);
      /*
      int n      = sc.nextInt();        // read input as integer
      long k     = sc.nextLong();       // read input as long
      double d   = sc.nextDouble();     // read input as double
      String str = sc.next();           // read input as String
      String s   = sc.nextLine();       // read whole line as String

      int result = 3*n;
      out.println(result);                    // print via PrintWriter
      */

      // Stop writing your solution here. -------------------------------------
      out.close();
   }

     

   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   }
   //--------------------------------------------------------
}