E. Long Permutationtime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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, \ldots, n]. In other words, a[i] = i (1 \le i \le 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] + \ldots + 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] \rightarrow [1, 4, 2, 3] \rightarrow [1, 4, 3, 2]. For each query of the 1-st type output the required sum.InputThe first line contains two integers n (2 \le n \le 2 \cdot 10^5) and q (1 \le q \le 2 \cdot 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 \le l \le r \le n), the 2-nd type query consists of two integers 2 and x (1 \le x \le 10^5).It is guaranteed that all requests of the 2-nd type are possible to process.OutputFor each query of the 1-st type, output on a separate line one integer — the required sum.ExampleInput
4 4
1 2 4
2 3
1 1 2
1 3 4
Output
9
4
6
NoteInitially, the permutation has the form [1, 2, 3, 4]. Queries processing is as follows:   2 + 3 + 4 = 9;  [1, 2, 3, 4] \rightarrow [1, 2, 4, 3] \rightarrow [1, 3, 2, 4] \rightarrow [1, 3, 4, 2];  1 + 3 = 4;  4 + 2 = 6 
4 4
1 2 4
2 3
1 1 2
1 3 4

9 4 6 
['brute force', 'math', 'two pointers', '*2400']