human
Can you solve the below in PYTHON3?
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...]
 What is 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.

# Sujith
from sys import stdin,stdout,setrecursionlimit
from io import BytesIO, IOBase
# from heapq import heappush as push,heappop as hp,heapify as h
# from math import gcd,floor,sqrt,ceil
# from collections import Counter,deque as dq
# from itertools import accumulate as acc,permutations as perm
# from bisect import bisect_left as bl,bisect_right as br,bisect as bis

setrecursionlimit(10000)

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        import os
        self.os = os
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
        self.BUFSIZE = 8192

    def read(self):
        while True:
            a = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, self.BUFSIZE))
            if not a:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(a), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            a = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, self.BUFSIZE))
            self.newlines = a.count(b"\n") + (not a)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(a), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            self.os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)

class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")

stdin, stdout =...