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:
n, q = map(int, input().split())
A = [i for i in range(1, n + 1)]

prefix = [0] * (n + 1)
prefix[0] = A[0]
for i in range(1, n):
    prefix[i] = prefix[i - 1] + A[i]
    
used0 = A[max(0, n - 15)::]
used0.sort()
used_d = {}
for i in used0:
    used_d[i] = 0
 
fact = [0] * n
fact[-1] = 1
for i in range(n - 2, max(-1, n - 16), -1):
    fact[i] = fact[i + 1] * (n - 1 - i)

number = 1
#print(fact)

def permutation_by_number(number):
    for i in range(max(0, n - 15), n):
        position = max(0, (number - 1) // fact[i])
        #print(position)
        counter = 0
        for j in used_d:
            if position == counter and not used_d[j]:
                A[i] = j
                used_d[j] = 1
                break
            if not used_d[j]:
                counter += 1
        number -= position * fact[i] 
    for i in range(max(0, n - 15), n):
        prefix[i] = prefix[i - 1] + A[i]
            
for i in range(q):
    #print(prefix, A, number)
    t = list(map(int, input().split()))   
    if t[0] == 1:
        l, r = t[1], t[2]
        print(prefix[r - 1] - prefix[l - 2])
    else:
        for j in used_d:
            used_d[j] = 0
        x = t[1]
        number += x
        permutation_by_number(number)