human
Give me a Python program to find the k-th special number if they are sorted in increasing order given the following:
PYTHON3 solution for "Theofanis really likes sequences of positive integers, thus his teacher (Yeltsa Kcir) gave him a problem about a sequence that consists of only special numbers.

Let's call a positive number special if it can be written as a sum of different non-negative powers of n. For example, for n = 4 number 17 is special, because it can be written as 4^0 + 4^2 = 1 + 16 = 17, but 9 is not.

Theofanis asks you to help him find the k-th special number if they are sorted in increasing order. Since this number may be too large, output it modulo 10^9+7.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first and only line of each test case contains two integers n and k (2 ≤ n ≤ 10^9.
1 ≤ k ≤ 10^9).

Output

For each test case, print one integer — the k-th special number in increasing order modulo 10^9+7.

Example

Input

3
3 4
2 12
105 564

Output

9
12
3595374

Note

For n = 3 the sequence is [1,3,4,9...]":
assistant
#Here is Python program to find the k-th special number if they are sorted in increasing order.
 import sys
def hp(n):
    while n%2==0:
        n=n//2
    if n==1:
        return True
    else:
        return False
try:
    m=10**9+7
    def main():
        n,k=map(int,input().split())
        ans=0
        x=bin(k)[2:][::-1]
        p=1
        ans=0
       
        for si in x:
            ans+=((p)*int(si))
            p=(p*n)

        print(int(ans%m))

        
        
        


except:
    pass

for _ in range(int(input())):
     main()