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 PYTHON3):

Solution:
import sys
input=sys.stdin.readline

fact=[1]
for i in range(1,15+1):
    fact.append(fact[-1]*i)

def generate_perm(n,m):
    ret=[]
    if n<=15:
        cand=[i+1 for i in range(n)]
    else:
        cand=[i+1 for i in range(n-15,n)]
    for i in range(1,min(15+1,n+1)):
        pos=m//fact[min(15,n)-i]
        m%=fact[min(15,n)-i]
        ret.append(cand[pos])
        del cand[pos]
    return ret

n,q=map(int,input().split())
ids=0
if n<=15:
    perm=[i+1 for i in range(n)]
else:
    perm=[i+1 for i in range(n-15,n)]
for _ in range(q):
    query=list(map(int,input().split()))
    if query[0]==1:
        l,r=query[1],query[2]
        if n<=15:
            print(sum(perm[l-1:r]))
        else:
            if l<=n-15:
                if r<=n-15:
                    print((r*(r+1))//2-(l*(l-1))//2)
                else:
                    print(((n-15)*(n-14))//2-(l*(l-1))//2+sum(perm[0:r-(n-15)]))
            else:
                print(sum(perm[l-1-(n-15):r-(n-15)]))
    elif query[0]==2:
        ids+=query[1]
        perm=generate_perm(n,ids)