Mikhail walks on a Cartesian plane. He starts at the point (0, 0), and in one move he can go to any of eight adjacent points. For example, if Mikhail is currently at the point (0, 0), he can go to any of the following points in one move: 

  * (1, 0); 
  * (1, 1); 
  * (0, 1); 
  * (-1, 1); 
  * (-1, 0); 
  * (-1, -1); 
  * (0, -1); 
  * (1, -1). 



If Mikhail goes from the point (x1, y1) to the point (x2, y2) in one move, and x1 ≠ x2 and y1 ≠ y2, then such a move is called a diagonal move.

Mikhail has q queries. For the i-th query Mikhail's target is to go to the point (n_i, m_i) from the point (0, 0) in exactly k_i moves. Among all possible movements he want to choose one with the maximum number of diagonal moves. Your task is to find the maximum number of diagonal moves or find that it is impossible to go from the point (0, 0) to the point (n_i, m_i) in k_i moves.

Note that Mikhail can visit any point any number of times (even the destination point!).

Input

The first line of the input contains one integer q (1 ≤ q ≤ 10^4) — the number of queries.

Then q lines follow. The i-th of these q lines contains three integers n_i, m_i and k_i (1 ≤ n_i, m_i, k_i ≤ 10^{18}) — x-coordinate of the destination point of the query, y-coordinate of the destination point of the query and the number of moves in the query, correspondingly.

Output

Print q integers. The i-th integer should be equal to -1 if Mikhail cannot go from the point (0, 0) to the point (n_i, m_i) in exactly k_i moves described above. Otherwise the i-th integer should be equal to the the maximum number of diagonal moves among all possible movements.

Example

Input

3
2 2 3
4 3 7
10 1 9


Output

1
6
-1

Note

One of the possible answers to the first test case: (0, 0) → (1, 0) → (1, 1) → (2, 2).

One of the possible answers to the second test case: (0, 0) → (0, 1) → (1, 2) → (0, 3) → (1, 4) → (2, 3) → (3, 2) → (4, 3).

In the third test case Mikhail cannot reach the point (10, 1) in 9 moves.
/*
 * 
 * @Author  Ajudiya_13(Bhargav Girdharbhai Ajudiya)
 * Dhirubhai Ambani Institute of Information And Communication Technology 
 * 
 */


import java.util.*;
import java.io.*;
import java.lang.*;

public class Code2
{
	
	public static void main(String[] args)
	{
		InputReader in = new InputReader(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int query = in.nextInt();
		for(int q=0;q<query;q++)
		{
			long n = in.nextLong();
			long m = in.nextLong();
			long k = in.nextLong();
			//System.out.println(n + " " + m + " " + k);
			long max = Math.max(n, m);
			if(max>k)
				pw.println("-1");
			else
			{
				if(n==m)
				{
					long  ans1 = n;
					long tk = k-n;
					if(tk%2==0)
						pw.println(ans1+tk);
					else
					{
						if(tk<=1)
							ans1--;
						else
						{
							tk-=3;
							ans1++;
							ans1+=(tk);
						}
						pw.println(ans1);
					}
				}
				else
				{
					long ans1 = n;
					long ans2 = m;
					long count1 = n;
					long count2 = m;
					count1 += Math.abs(n-m);
					count2 += Math.abs(n-m);
					long tk1 = k - count1;
					long tk2 = k - count2;
					//System.out.println(tk1 + " " + tk2);
					if(tk1%2==0)
						ans1 += tk1;
					else
					{
						if(tk1<=1)
							ans1++;
						else
						{
							tk1-=3;
							ans1++;
							ans1+=(tk1);
						}
					}
					
					if(tk2%2==0)
						ans2 += (tk2);
					else
					{
						if(tk2<=1)
							ans2++;
						else
						{
							tk2-=3;
							ans2++;
							ans2+=(tk2);
						}
					}
					
					pw.println(Math.max(ans1, ans2));
				}
			}
		}
		pw.flush();
		pw.close();
	}
	
	static class InputReader 
	{
		 
		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) 
		{
			this.stream = stream;
		}
 
		public int snext() 
		{
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) 
			{
				curChar = 0;
				try 
				{
					snumChars = stream.read(buf);
				} 
				catch (IOException e) 
				{
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public int nextInt() 
	    {
			int c = snext();
			while (isSpaceChar(c)) 
			{
				c = snext();
			}
			int sgn = 1;
			if (c == '-')
		    {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public long nextLong()
	    {
			int c = snext();
			while (isSpaceChar(c)) 
			{
				c = snext();
			}
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public int[] nextIntArray(int n) 
		{
			int a[] = new int[n];
			for (int i = 0; i < n; i++) 
			{
				a[i] = nextInt();
			}
			return a;
		}
 
		public String readString()
	    {
			int c = snext();
			while (isSpaceChar(c)) 
			{
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public String nextLine() 
		{
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c) 
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		private boolean isEndOfLine(int c) 
		{
			return c == '\n' || c == '\r' || c == -1;
		}
 
		public interface SpaceCharFilter
	    {
			public boolean isSpaceChar(int ch);
		}
	}
	
	public static long mod = 1000000007;
	public static int d;
	public static int p;
	public static int q;
	
	public static int[] suffle(int[] a,Random gen)
	{
		int n = a.length;
		for(int i=0;i<n;i++)
		{
			int ind = gen.nextInt(n-i)+i;
			int temp = a[ind];
			a[ind] = a[i];
			a[i] = temp;
		}
		return a;
	}
	
	public static void swap(int a, int b){
		int temp = a;
		a = b;
		b = temp;
	}
	
	public static HashSet<Integer> primeFactorization(int n)
	{
		HashSet<Integer> a =new HashSet<Integer>();
		for(int i=2;i*i<=n;i++)
		{
			while(n%i==0)
			{
				a.add(i);
				n/=i;
			}
		}
		if(n!=1)
			a.add(n);
		return a;
	}
	
	public static void sieve(boolean[] isPrime,int n)
	{
		for(int i=1;i<n;i++)
			isPrime[i] = true;
		
		isPrime[0] = false;
		isPrime[1] = false;
		
		for(int i=2;i*i<n;i++)
		{
			if(isPrime[i] == true)
			{
				for(int j=(2*i);j<n;j+=i)
					isPrime[j] = false;
			}
		}
	}
	
	public static int GCD(int a,int b)
	{
		if(b==0)
			return a;
		else
			return GCD(b,a%b);
	}
	
	public static long GCD(long a,long b)
	{
		if(b==0)
			return a;
		else
			return GCD(b,a%b);
	}
	
	public static void extendedEuclid(int A,int B)
	{
		if(B==0)
		{
			d = A;
			p = 1 ;
			q = 0;
		}
		else
		{
			extendedEuclid(B, A%B);
			int temp = p;
			p = q;
			q = temp - (A/B)*q;
		}
	}
	
	public static long LCM(long a,long b)
	{
		return (a*b)/GCD(a,b);
	}
	
	public static int LCM(int a,int b)
	{
		return (a*b)/GCD(a,b);
	}
	
	public static int binaryExponentiation(int x,int n)
	{
	    int result=1;
	    while(n>0)
	    {
	        if(n % 2 ==1)
	            result=result * x;
	        x=x*x;
	        n=n/2;
	    }
	    return result;
	}
	
	public static long binaryExponentiation(long x,long n)
	{
	    long result=1;
	    while(n>0)
	    {
	        if(n % 2 ==1)
	            result=result * x;
	        x=x*x;
	        n=n/2;
	    }
	    return result;
	}
	
	public static int modularExponentiation(int x,int n,int M)
	{
	    int result=1;
	    while(n>0)
	    {
	        if(n % 2 ==1)
	            result=(result * x)%M;
	        x=(x*x)%M;
	        n=n/2;
	    }
	    return result;
	}
	
	public static long modularExponentiation(long x,long n,long M)
	{
	    long result=1;
	    while(n>0)
	    {
	        if(n % 2 ==1)
	            result=(result * x)%M;
	        x=(x*x)%M;
	        n=n/2;
	    }
	    return result;
	}
	
	public static int modInverse(int A,int M)
	{
	    return modularExponentiation(A,M-2,M);
	}
	
	public static long modInverse(long A,long M)
	{
	    return modularExponentiation(A,M-2,M);
	}
	
	public static boolean isPrime(int n)
	{
	    
	    if (n <= 1)  return false;
	    if (n <= 3)  return true;
	    
	    if (n%2 == 0 || n%3 == 0) 
	    	return false;
	 
	    for (int i=5; i*i<=n; i=i+6)
	    {
	        if (n%i == 0 || n%(i+2) == 0)
	           return false;
	    }
	    
	    return true;
	}
	
	static class pair implements Comparable<pair>
	{
		Integer x, y;
		pair(int x,int y)
		{
			this.x=x;
			this.y=y;
		}
		
		public int compareTo(pair o) {
			int result = x.compareTo(o.x);
			if(result==0)
				result = y.compareTo(o.y);
			
			return result;
		}  
		
		public String toString()
		{
			return x+" "+y;
		}
		
		public boolean equals(Object o)
		{
			if (o instanceof pair)
		    {
				pair p = (pair)o;
				return (Math.abs(p.x-x)==0 && Math.abs(p.y-y)==0);
			}
			return false;
		}
		
		public int hashCode()
		{
			return new Long(x).hashCode()*31 + new Long(y).hashCode();
		}
	}
}