write a go solution for Description:
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,ldots,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]+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]arrow[1,4,2,3]arrow[1,4,3,2].

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

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

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]arrow[1,2,4,3]arrow[1,3,2,4]arrow[1,3,4,2];
3. 1+3=4;
4. 4+2=6. Output only the code with no comments, explanation, or additional text.