#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a / gcd(a, b) * b); }
bool sorta(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.second < b.second);
}
bool sortd(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.second > b.second);
}
void printarr(long long arr[], long long n) {
  for (int i = 0; i < n; i++) cout << arr[i] << " ";
  cout << "\n";
}
string decToBinary(int n) {
  string s = "";
  int i = 0;
  while (n > 0) {
    s = to_string(n % 2) + s;
    n = n / 2;
    i++;
  }
  return s;
}
long long binaryToDecimal(string n) {
  string num = n;
  long long dec_value = 0;
  int base = 1;
  int len = num.length();
  for (int i = len - 1; i >= 0; i--) {
    if (num[i] == '1') dec_value += base;
    base = base * 2;
  }
  return dec_value;
}
bool isPrime(int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
bool isPowerOfTwo(int n) {
  if (n == 0) return false;
  return (ceil(log2(n)) == floor(log2(n)));
}
bool isPerfectSquare(long long x) {
  if (x >= 0) {
    long long sr = sqrt(x);
    return (sr * sr == x);
  }
  return false;
}
long long moduloMultiplication(long long a, long long b, long long mod) {
  long long res = 0;
  a %= mod;
  while (b) {
    if (b & 1) res = (res + a) % mod;
    b >>= 1;
  }
  return res;
}
long long powermod(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
void asquare() {
  long long mod = 1000000007;
  long long n, k;
  cin >> n >> k;
  if (isPowerOfTwo(k)) {
    cout << powermod(n, ceil(log2(k)), mod) << "\n";
  } else {
    long long c = 0;
    while (k > 0) {
      if (k == 1) {
        c++;
        k = 0;
      } else if (k == 2) {
        c += n % mod;
        k = 0;
      } else if (k == 3) {
        c += (n + 1) % mod;
        k = 0;
      } else if (isPowerOfTwo(k)) {
        c += powermod(n, ceil(log2(k)), mod);
        k = 0;
      } else {
        long long x = pow(2, floor(log2(k)));
        c += powermod(n, floor(log2(k)), mod);
        k -= x;
      }
    }
    cout << c % mod << "\n";
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t;
  cin >> t;
  while (t--) {
    asquare();
  }
  return 0;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

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...]

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a / gcd(a, b) * b); }
bool sorta(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.second < b.second);
}
bool sortd(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.second > b.second);
}
void printarr(long long arr[], long long n) {
  for (int i = 0; i < n; i++) cout << arr[i] << " ";
  cout << "\n";
}
string decToBinary(int n) {
  string s = "";
  int i = 0;
  while (n > 0) {
    s = to_string(n % 2) + s;
    n = n / 2;
    i++;
  }
  return s;
}
long long binaryToDecimal(string n) {
  string num = n;
  long long dec_value = 0;
  int base = 1;
  int len = num.length();
  for (int i = len - 1; i >= 0; i--) {
    if (num[i] == '1') dec_value += base;
    base = base * 2;
  }
  return dec_value;
}
bool isPrime(int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
bool isPowerOfTwo(int n) {
  if (n == 0) return false;
  return (ceil(log2(n)) == floor(log2(n)));
}
bool isPerfectSquare(long long x) {
  if (x >= 0) {
    long long sr = sqrt(x);
    return (sr * sr == x);
  }
  return false;
}
long long moduloMultiplication(long long a, long long b, long long mod) {
  long long res = 0;
  a %= mod;
  while (b) {
    if (b & 1) res = (res + a) % mod;
    b >>= 1;
  }
  return res;
}
long long powermod(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
void asquare() {
  long long mod = 1000000007;
  long long n, k;
  cin >> n >> k;
  if (isPowerOfTwo(k)) {
    cout << powermod(n, ceil(log2(k)), mod) << "\n";
  } else {
    long long c = 0;
    while (k > 0) {
      if (k == 1) {
        c++;
        k = 0;
      } else if (k == 2) {
        c += n % mod;
        k = 0;
      } else if (k == 3) {
        c += (n + 1) % mod;
        k = 0;
      } else if (isPowerOfTwo(k)) {
        c += powermod(n, ceil(log2(k)), mod);
        k = 0;
      } else {
        long long x = pow(2, floor(log2(k)));
        c += powermod(n, floor(log2(k)), mod);
        k -= x;
      }
    }
    cout << c % mod << "\n";
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t;
  cin >> t;
  while (t--) {
    asquare();
  }
  return 0;
}

```