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...]":



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Can you provide a Python program to find the k-th special number if they are sorted in increasing order?
assistant
#Here is Python program to find the k-th special number if they are sorted in increasing order.
 def ans(k,a):
    x = 0
    while k>a:
        a = a + 2**x
        x+=1
    k = k - 2**(x-1)
    return (x-1,k)
for _ in range(int(input())):
    n, k  = map(int, input().split())
    a = 0
    y = 0
    while k !=0:
        p,k = ans(k,a)
        y = y + n**p
    print(y%((10**9)+7))