1284_C. New Year and Permutation
Recall that the permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).

A sequence a is a subsegment of a sequence b if a can be obtained from b by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. We will denote the subsegments as [l, r], where l, r are two integers with 1 ≤ l ≤ r ≤ n. This indicates the subsegment where l-1 elements from the beginning and n-r elements from the end are deleted from the sequence.

For a permutation p_1, p_2, …, p_n, we define a framed segment as a subsegment [l,r] where max\\{p_l, p_{l+1}, ..., p_r\} - min\\{p_l, p_{l+1}, ..., p_r\} = r - l. For example, for the permutation (6, 7, 1, 8, 5, 3, 2, 4) some of its framed segments are: [1, 2], [5, 8], [6, 7], [3, 3], [8, 8]. In particular, a subsegment [i,i] is always a framed segments for any i between 1 and n, inclusive.

We define the happiness of a permutation p as the number of pairs (l, r) such that 1 ≤ l ≤ r ≤ n, and [l, r] is a framed segment. For example, the permutation [3, 1, 2] has happiness 5: all segments except [1, 2] are framed segments.

Given integers n and m, Jongwon wants to compute the sum of happiness for all permutations of length n, modulo the prime number m. Note that there exist n! (factorial of n) different permutations of length n.

Input

The only line contains two integers n and m (1 ≤ n ≤ 250 000, 10^8 ≤ m ≤ 10^9, m is prime).

Output

Print r (0 ≤ r < m), the sum of happiness for all permutations of length n, modulo a prime number m.

Examples

Input


1 993244853


Output


1


Input


2 993244853


Output


6


Input


3 993244853


Output


32


Input


2019 993244853


Output


923958830


Input


2020 437122297


Output


265955509

Note

For sample input n=3, let's consider all permutations of length 3:

  * [1, 2, 3], all subsegments are framed segment. Happiness is 6. 
  * [1, 3, 2], all subsegments except [1, 2] are framed segment. Happiness is 5. 
  * [2, 1, 3], all subsegments except [2, 3] are framed segment. Happiness is 5. 
  * [2, 3, 1], all subsegments except [2, 3] are framed segment. Happiness is 5. 
  * [3, 1, 2], all subsegments except [1, 2] are framed segment. Happiness is 5. 
  * [3, 2, 1], all subsegments are framed segment. Happiness is 6. 



Thus, the sum of happiness is 6+5+5+5+5+6 = 32.
```python
n, m = map(int, input().split())

fac = [1]
for i in range(1, n + 1):
    fac.append(i * fac[i - 1] % m)
ans = 0
for i in range(1, n+1):
    ans += (n - i + 1) * fac[i] * fac[n - i + 1]
    ans %= m
print(ans)

```