Problem: A permutation is a sequence of integers from 1 to n of length n containing each number exactly once. For example, [1], [4, 3, 5, 1, 2], [3, 2, 1] — are permutations, and [1, 1], [4, 3, 1], [2, 3, 4] — no.

Permutation a is lexicographically smaller than permutation b (they have the same length n), if in the first index i in which they differ, a[i] < b[i]. For example, the permutation [1, 3, 2, 4] is lexicographically smaller than the permutation [1, 3, 4, 2], because the first two elements are equal, and the third element in the first permutation is smaller than in the second.

The next permutation for a permutation a of length n — is the lexicographically smallest permutation b of length n that lexicographically larger than a. For example: 

  * for permutation [2, 1, 4, 3] the next permutation is [2, 3, 1, 4]; 
  * for permutation [1, 2, 3] the next permutation is [1, 3, 2]; 
  * for permutation [2, 1] next permutation does not exist. 



You are given the number n — the length of the initial permutation. The initial permutation has the form a = [1, 2, …, n]. In other words, a[i] = i (1 ≤ i ≤ n).

You need to process q queries of two types: 

  * 1 l r: query for the sum of all elements on the segment [l, r]. More formally, you need to find a[l] + a[l + 1] + … + a[r]. 
  * 2 x: x times replace the current permutation with the next permutation. For example, if x=2 and the current permutation has the form [1, 3, 4, 2], then we should perform such a chain of replacements [1, 3, 4, 2] → [1, 4, 2, 3] → [1, 4, 3, 2]. 



For each query of the 1-st type output the required sum.

Input

The first line contains two integers n (2 ≤ n ≤ 2 ⋅ 10^5) and q (1 ≤ q ≤ 2 ⋅ 10^5), where n — the length of the initial permutation, and q — the number of queries.

The next q lines contain a single query of the 1-st or 2-nd type. The 1-st type query consists of three integers 1, l and r (1 ≤ l ≤ r ≤ n), the 2-nd type query consists of two integers 2 and x (1 ≤ x ≤ 10^5).

It is guaranteed that all requests of the 2-nd type are possible to process.

Output

For each query of the 1-st type, output on a separate line one integer — the required sum.

Example

Input


4 4
1 2 4
2 3
1 1 2
1 3 4


Output


9
4
6

Note

Initially, the permutation has the form [1, 2, 3, 4]. Queries processing is as follows: 

  1. 2 + 3 + 4 = 9; 
  2. [1, 2, 3, 4] → [1, 2, 4, 3] → [1, 3, 2, 4] → [1, 3, 4, 2]; 
  3. 1 + 3 = 4; 
  4. 4 + 2 = 6 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
inline int read(void) {
  char ch = getchar();
  int ans = 0;
  while (!isdigit(ch)) ch = getchar();
  while (isdigit(ch)) ans = ans * 10 + ch - '0', ch = getchar();
  return ans;
}
const int N = 2e5 + 7;
int n, m;
long long rk, prefix[N], fac[20];
void init(void) {
  rk = 0;
  for (int i = fac[0] = 1; i < 20; ++i) fac[i] = fac[i - 1] * i;
}
void solve(int x) {
  rk += x;
  long long tmp = rk;
  int len = 0;
  vector<int> v, ans;
  for (int i = 14; i >= 0; --i) {
    if (!len && tmp < fac[i]) continue;
    if (!len) {
      len = i + 1;
      for (int j = n - len + 1; j <= n; ++j) v.push_back(j);
    }
    int num = tmp / fac[i];
    tmp %= fac[i];
    ans.push_back(v[num]);
    v.erase(v.begin() + num);
  }
  for (int i = n - len + 1, j = 0; i <= n; ++i, ++j) {
    prefix[i] = prefix[i - 1] + ans[j];
  }
}
int main(void) {
  init();
  n = read(), m = read();
  for (int i = 1; i <= n; ++i) prefix[i] += prefix[i - 1] + i;
  for (int i = 1; i <= m; ++i) {
    int op = read();
    if (op == 1) {
      int l = read(), r = read();
      printf("%lld\n", prefix[r] - prefix[l - 1]);
    } else {
      int x;
      cin >> x;
      solve(x);
    }
  }
  return 0;
}