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 q1;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Q1 {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		Reader.init(System.in);
		//PrintWriter  out= new PrintWriter(System.out);
		int t=Reader.nextInt();
		for(int i=0;i<t;i++) {
			int stick=Reader.nextInt();
			int diamond=Reader.nextInt();
			long tot=0;
			while((stick>0 && diamond >1) || (stick>1  && diamond>0)) {
				
				 if(stick >=2*diamond) {
					tot+=diamond;
					diamond=0;
					stick-=(2*diamond);
				}
				 else if(diamond>=2*stick) {
					 tot+=stick;
					 stick=0;
					 diamond-=(2*stick);
				 }
				 else if(stick == diamond) {
					 int d=stick/3;
					 int r=stick%3;
					 tot+=(2*d);
					 stick-=(3*d);
					 diamond-=(3*d);
					 if(r ==2) {
						 tot++;
						 stick=0;
						 diamond=0;
					 }
				 }
				 else if(stick>diamond) {
						int d=stick-diamond;
					 	stick-=(2*d);
						diamond-=d;
						tot+=d;
				}	
				else if(stick<diamond){
					//int d=Math.min(stick/2, diamond/2);
					int d=diamond-stick;
					tot+=d;
					stick-=d;
					diamond-=(2*d);
				}
			//	System.out.println(tot+" "+ stick +" "+diamond);
		}
			System.out.println(tot);
			//out.append(tot);
			//out.flush();

	}

}
}
class Reader {
	 static BufferedReader reader;
	 static StringTokenizer tokenizer;
	 /** call this method to initialize reader for InputStream */
	 static void init(InputStream input) {
	 reader = new BufferedReader(
	 new InputStreamReader(input) );
	 tokenizer = new StringTokenizer("");
	 }
	 /** get next word */
	 static String next() throws IOException {
	 while ( ! tokenizer.hasMoreTokens() ) {
	 //TODO add check for eof if necessary
	 tokenizer = new StringTokenizer(
	 reader.readLine() );
	 }
	 return tokenizer.nextToken();
	 }
	 static int nextInt() throws IOException {
	 return Integer.parseInt( next() );
	 }
	 static long nextLong() throws IOException {
		 return Long.parseLong( next() );
		 }
	 static double nextDouble() throws IOException {
	 return Double.parseDouble( next() );
	 }
	}
