Problem: You are given two positive integers n and k. Print the k-th positive integer that is not divisible by n.

For example, if n=3, and k=7, then all numbers that are not divisible by 3 are: 1, 2, 4, 5, 7, 8, 10, 11, 13 .... The 7-th number among them is 10.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Next, t test cases are given, one per line.

Each test case is two positive integers n (2 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 10^9).

Output

For each test case print the k-th positive integer that is not divisible by n.

Example

Input


6
3 7
4 12
2 1000000000
7 97
1000000000 1000000000
2 1


Output


10
15
1999999999
113
1000000001
1

Solution (in PYTHON3):

Solution:
"""
t=int(input())
for _ in range(t):
    #n=int(input())
    n,k=list(map(int,input().split()))
    if n<k:
        print("NO")
        continue
    if n%2==1 and k%2==1:
        print("YES")
        print(*([1]*(k-1)+[n-k+1]))
    elif n%2==1:
        print("NO")
    else:
        arr=[2]*(k-1)+[n-k-k+2]
        if n-2*k+2<0:
            print("NO")
        else:
            print("YES")
            print(*arr)
    
    
"""
import math
#123 567 91011 131415
#123 456 789 101112
#12 45 78 1011
#12 34 56 78
t=int(input())
for _ in range(t):
    #n=int(input())
    n,k=list(map(int,input().split()))
    #arr=[i for i in range(1,n)]
    vv=math.ceil(k/(n-1))
    val=k%(n-1)
    if val==0:
        val=n-1
    #print(val)
    print(1+n*(vv-1)+val-1)