Polycarp plays a well-known computer game (we won't mention its name). In this game, he can craft tools of two types — shovels and swords. To craft a shovel, Polycarp spends two sticks and one diamond; to craft a sword, Polycarp spends two diamonds and one stick.

Each tool can be sold for exactly one emerald. How many emeralds can Polycarp earn, if he has a sticks and b diamonds?

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

The only line of each test case contains two integers a and b (0 ≤ a, b ≤ 10^9) — the number of sticks and the number of diamonds, respectively.

Output

For each test case print one integer — the maximum number of emeralds Polycarp can earn.

Example

Input


4
4 4
1000000000 0
7 15
8 7


Output


2
0
7
5

Note

In the first test case Polycarp can earn two emeralds as follows: craft one sword and one shovel.

In the second test case Polycarp does not have any diamonds, so he cannot craft anything.
//package com.codeforces.eclipse;
import java.io.*;
import java.util.*;
public class Shovels {
	static class Reader {
	    static BufferedReader reader;
	    static StringTokenizer tokenizer;

	    static void init(InputStream input) {
	        reader = new BufferedReader(
	                     new InputStreamReader(input) );
	        tokenizer = new StringTokenizer("");
	    }

	    static String next() throws IOException {
	        while ( ! tokenizer.hasMoreTokens() ) {
	            tokenizer = new StringTokenizer(
	                   reader.readLine() );
	        }
	        return tokenizer.nextToken();
	    }

	    static int nextInt() throws IOException {
	        return Integer.parseInt(next());
	    }
		
	    static double nextDouble() throws IOException {
	        return Double.parseDouble(next());
	    }
	    static long nextLong() throws IOException {
	    	return Long.parseLong(next());
	    }
	}
	public static void main(String[] args) throws IOException {
		Reader.init(System.in);
		int t = Reader.nextInt();
		while(t-->0) {
			int a = Reader.nextInt();
			int b = Reader.nextInt();
			int ans = Math.min(Math.min(a,b),(a+b)/3);
			System.out.println(ans);
		}
	}
}
