human
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.
 def power(n,y,m=1000000007):
   n %= m
   res = 1
   while(y > 0):
      if(y & 1):
         res = res * n % m
      n = n * n % m
      y >>= 1
   
   return res
t = int(input())
for tc in range(t):
   n,k = map(int,input().split())
   s = bin(k)
   s = s[2:]
   a = 32-len(s)
   s='0'*(a)+s
   ans = 0
   s = s[::-1]
   for i in range(32):
      if(s[i]=='1'):
         ans=(ans+power(n, i))%1000000007
   print(ans)