Carol wants to win Cactus' heart, so she has planned a magnificent trip to the land of Cartesia together. Unfortunately, Cactus is not very interested in the modern art and hiking trails, nor Cartesia's mystical scripture of calculating time complexity. He is more preoccupied with solving an abstract algorithm problem. Carol decides to solve the following problem for him.

A contiguous subsequence of an array is a sequence of numbers at indices of the array. An increasing contiguous subsequence of an array is a contiguous subsequence where .

Cactus would like to know the number of permutations of the elements to where the maximum length increasing contiguous subsequence has length .

#### Constraints

##### Subtask 1 [7/15]

##### Subtask 2 [8/15]

No additional constraints.

#### Input Specification

The first line will contain and .

#### Output Specification

Output the number of permutations of the elements to which has maximum contiguous increasing subsequence with length , mod .

#### Sample Input 1

`5 3`

#### Sample Output 1

`41`

#### Sample Input 2

`10 8`

#### Sample Output 2

`231`

#### Sample Input 3

`1 1`

#### Sample Output 3

`1`

## Comments