You are given two integers n and m. Find the \operatorname{MEX} of the sequence n ⊕ 0, n ⊕ 1, …, n ⊕ m. Here, ⊕ is the [bitwise XOR operator](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

\operatorname{MEX} of the sequence of non-negative integers is the smallest non-negative integer that doesn't appear in this sequence. For example, \operatorname{MEX}(0, 1, 2, 4) = 3, and \operatorname{MEX}(1, 2021) = 0. 

Input

The first line contains a single integer t (1 ≤ t ≤ 30 000) — the number of test cases.

The first and only line of each test case contains two integers n and m (0 ≤ n, m ≤ 10^9).

Output

For each test case, print a single integer — the answer to the problem.

Example

Input


5
3 5
4 6
3 2
69 696
123456 654321


Output


4
3
0
640
530866

Note

In the first test case, the sequence is 3 ⊕ 0, 3 ⊕ 1, 3 ⊕ 2, 3 ⊕ 3, 3 ⊕ 4, 3 ⊕ 5, or 3, 2, 1, 0, 7, 6. The smallest non-negative integer which isn't present in the sequence i. e. the \operatorname{MEX} of the sequence is 4.

In the second test case, the sequence is 4 ⊕ 0, 4 ⊕ 1, 4 ⊕ 2, 4 ⊕ 3, 4 ⊕ 4, 4 ⊕ 5, 4 ⊕ 6, or 4, 5, 6, 7, 0, 1, 2. The smallest non-negative integer which isn't present in the sequence i. e. the \operatorname{MEX} of the sequence is 3.

In the third test case, the sequence is 3 ⊕ 0, 3 ⊕ 1, 3 ⊕ 2, or 3, 2, 1. The smallest non-negative integer which isn't present in the sequence i. e. the \operatorname{MEX} of the sequence is 0.
import java.io.*;
import java.util.*;

public class Main{
	static void main() throws Exception{
	    int n=sc.nextInt(),m=sc.nextInt();
	    
	    if(n==0) {
	    	pw.println(m+1);
	    	return;
	    }
	    long x=(Integer.highestOneBit(n)*1l)<<1;
	    long cnt=m/x;
	    long rem=m%x;
	    long ans=cnt*x;
	    if(rem==x-1) {
	    	rem=0;
	    	ans+=x;
	    }
	    if(rem<n){
	        pw.println(ans);
	        return;
	    }
	    long dif=rem-n;
	    long o=1;
	    while((o&n)!=0 || (o<<1)<=dif)o<<=1;
	    pw.println(ans+Math.max(o, dif+1));
	}
	static int c=0;
	public static void main(String[] args) throws Exception{
		sc=new MScanner(System.in);
		pw = new PrintWriter(System.out);
		
		int tc=1;
        tc=sc.nextInt();
		for(int i=1;i<=tc;i++) {
			c=i;
//			pw.printf("Case #%d: ", i);
			main();
		}
		pw.flush();
	}
	static PrintWriter pw;
	static MScanner sc;
	static class MScanner {
		StringTokenizer st;
		BufferedReader br;
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
	 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
	 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int[] intArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public long[] longArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public int[] intSortedArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public long[] longSortedArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public Integer[] IntegerArr(int n) throws IOException {
	        Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public Long[] LongArr(int n) throws IOException {
	        Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
	 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
	 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
	 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
	 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
	 
		public boolean ready() throws IOException {
			return br.ready();
		}
	 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
		
	}
	static void dbg(int[]in) {
		System.out.println(Arrays.toString(in));
	}
	static void dbg(long[]in) {
		System.out.println(Arrays.toString(in));
	}
	static void sort(int[]in) {
		shuffle(in);
		Arrays.sort(in);
	}
	static void sort(long[]in) {
		shuffle(in);
		Arrays.sort(in);
	}
	static void shuffle(int[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*in.length);
			int tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
	static void shuffle(long[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*in.length);
			long tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
}