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.
# -*- coding: utf-8 -*-
"""
@author: Saurav Sihag
"""

rr = lambda: input().strip()
rri = lambda: int(rr())
# rri = lambda: int(stdin.readline())
rrm = lambda: [int(x) for x in rr().split()]
# stdout.write(str()+'\n')

from sys import stdin, stdout


def sol():
    x, y=rrm()
    res=0
    while x>4 and y>4:
        if x<y:
            a=x//4
            res+=a
            x-=a
            y-=2*a
        else:
            a=y//4;
            res+=a
            y-=a
            x-=2*a
    while (x>0 and y>1) or (y>0 and x>1):
        if x<y:
            if x==1:
                res+=1
                break
            a=x//2
            res+=a
            x-=a
            y-=2*a
        else:
            if y==1:
                res+=1
                break
            a=y//2;
            res+=a
            y-=a
            x-=2*a
    print(res)
    return


# sol()
T = rri()
for t in range(1, T + 1):
    ans = sol()
    # print("Case #{}: {}".format(t, ans))

