시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 (추가 시간 없음) 512 MB 1 1 1 100.000%

## 문제

A palindrome is a string that reads the same backward as forward. For example, rotator, lil and abba are palindromes, but shalash is not.

A double palindrome is a string that is either a palindrome or a concatenation of two (not necessarily distinct) palindromes. For example, susanna, potato and abba are double palindromes, but zzyzx and abaabb are not.

Dalila has just realized that her name is a double palindrome! Now she wonders how many non-empty strings of length at most n composed of the first k English letters have the same property. Help her find this number and output it modulo 998 244 353.

## 입력

The only line contains two integers n and k — the maximum length of the string and the size of the alphabet (1 ≤ n ≤ 105; 1 ≤ k ≤ 26).

## 출력

Output the number of non-empty double palindromes of length at most n composed of the first k English letters, modulo 998 244 353.

## 예제 입력 1

3 3


## 예제 출력 1

33


## 예제 입력 2

6 2


## 예제 출력 2

114


## 예제 입력 3

42 7


## 예제 출력 3

83419789


## 힌트

In the first example the strings to be counted are: a, b, c, aa, ab, ac, ba, bb, bc, ca, cb, cc, aaa, aab, aac, aba, abb, aca, acc, baa, bab, bba, bbb, bbc, bcb, bcc, caa, cac, cbb, cbc, cca, ccb, ccc.