문제
Every day the express train goes past the farm. It has
Usually, Bessie watches the train go by, tracking the carriage labels. But today is too foggy, and Bessie can't see any of the labels! Luckily, she has acquired the sliding window minimums of the sequence of carriage labels, from a reputable source in the city. In particular, she has a positive integer
Help Bessie figure out the number of ways to assign a label to each carriage, consistent with the sliding window minimums. Since this number may be very large, Bessie will be satisfied if you find its remainder modulo
Bessie's information is completely reliable; that is, it is guaranteed that there is at least one consistent way to assign labels.
Problem credits: Dhruv Rohatgi
입력
The first line consists of two space-separated integers,
출력
A single integer: the number of ways, modulo
예제1
4 2
999999998
999999999
999999998
3