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:
# No need to use segment Tree because apart from the last 14 numbers, nothing will change since 14! > 2*pow(10, 10)

def modify(rest):
	for i in range(len(rest)):
		prefix[-len(rest)+i] = prefix[-len(rest)+(i-1)] + rest[i]
	# print("prefix", prefix)


def next_perm_direct(permc):	# Gets the next permc lexographically bigger permutation
	rest = [x for x in range(max(1, n-14), n+1)]

	temp = 1
	for i in range(1, len(rest)):
		temp = temp*i

	for i in range(len(rest)-1):
		if permc >= temp:
			change = permc//temp
			rest[i], rest[i+change] = rest[i+change], rest[i]
			rest = rest[:i+1] + list(sorted(rest[i+1:]))
			permc = permc%temp
		temp = temp//(len(rest)-1-i)
	# print("rest", rest)
	modify(rest)


n, q = map(int, input().split())
prefix = [0 for i in range(n+1)]
for i in range(1, n+1):
	prefix[i] = prefix[i-1]+i
# print(prefix)

permc = 0
for _ in range(q):
	quer = list(map(int, input().split()))
	if len(quer) == 2:
		permc += quer[1]
		next_perm_direct(permc)
	else:
		l, r = quer[1], quer[2]
		print(prefix[r]-prefix[l-1])