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 ll = long long;
using namespace std;
const int N = 1e6 + 10;
const int Mod = 0;
ll a[N], sum[N], p[N];
int n, m, T, q;
int Read();
void update(ll x) {
  vector<ll> v;
  x--;
  int cnt = 0;
  if (n <= 14) {
    for (int i = 1; i <= 14; i++) v.push_back(i);
  } else {
    for (int i = 1; i <= 14; i++) v.push_back(n - 14 + i);
  }
  for (int i = min(13, n - 1); i >= 0; i--) {
    int j = x / p[i];
    a[++cnt] = v[j];
    x %= p[i];
    v.erase(v.begin() + j);
  }
  int st = max(n - 13, 1);
  for (int i = st, xx = 1; i <= n; i++, xx++) {
    sum[i] = sum[i - 1] + a[xx];
  }
}
int main() {
  n = Read(), q = Read();
  for (int i = 1; i <= n; ++i) {
    a[i] = i;
    sum[i] = sum[i - 1] + i;
  }
  p[0] = 1;
  for (int i = 1; i <= 14; i++) p[i] = p[i - 1] * i;
  ll now = 1;
  for (int i = 1; i <= q; i++) {
    int opt;
    opt = Read();
    if (opt == 1) {
      int x = Read(), y = Read();
      printf("%lld\n", sum[y] - sum[x - 1]);
    } else {
      int x = Read();
      now += x;
      update(now);
    }
  }
  return 0;
}
int Read() {
  int val = 0, opt = 1;
  char ch;
  while (!isdigit(ch = getchar()))
    if (ch == '-') opt = -1;
  while (isdigit(ch)) (val *= 10) += ch - '0', ch = getchar();
  return val * opt;
}