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.
t=int(input())
for _ in range(t):
    a,b=map(int,input().split())
    print(min(a,b,int((a+b)/3)))



# t=int(input())
# for _ in range(t):
#     a,b=map(int,input().split())
#     c=0
#     while (a>=1 and b>=2) or (a>=2 and b>=1):
#         if a>=b:
#             a-=2
#             b-=1
#             c+=1
#         else:
#             a-=1
#             b-=2
#             c+=1
#         # print(a,b,c)
        
#     print(c)
#     # if b<int(a/2):
#     #     ans=b
#     #     f=1
#     # else:
#     #     ans=int(a/2)
#     #     f=0
#     # if f==0:
#     #     b-=ans
#     #     a-=ans
#     #     if b>2:
#     #         ans+=1
#     # print(ans)


    
