Problem:
Score : 400 points

Problem Statement

There are N cells arranged in a row, numbered 1, 2, \ldots, N from left to right.

Tak lives in these cells and is currently on Cell 1. He is trying to reach Cell N by using the procedure described below.

You are given an integer K that is less than or equal to 10, and K non-intersecting segments [L_1, R_1], [L_2, R_2], \ldots, [L_K, R_K].
Let S be the union of these K segments.
Here, the segment [l, r] denotes the set consisting of all integers i that satisfy l \leq i \leq r.

When you are on Cell i, pick an integer d from S and move to Cell i + d. You cannot move out of the cells.

To help Tak, find the number of ways to go to Cell N, modulo 998244353.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq K \leq \min(N, 10)

1 \leq L_i \leq R_i \leq N

[L_i, R_i] and [L_j, R_j] do not intersect (i \neq j)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
L_1 R_1
L_2 R_2
:
L_K R_K

Output

Print the number of ways for Tak to go from Cell 1 to Cell N, modulo 998244353.

Sample Input 1

5 2
1 1
3 4

Sample Output 1

4

The set S is the union of the segment [1, 1] and the segment [3, 4], therefore S = \{ 1, 3, 4 \} holds.

There are 4 possible ways to get to Cell 5:

1 \to 2 \to 3 \to 4 \to 5,

1 \to 2 \to 5,

1 \to 4 \to 5 and

1 \to 5.

Sample Input 2

5 2
3 3
5 5

Sample Output 2

0

Because S = \{ 3, 5 \} holds, you cannot reach to Cell 5.
Print 0.

Sample Input 3

5 1
1 2

Sample Output 3

5

Sample Input 4

60 3
5 8
1 3
10 15

Sample Output 4

221823067

Note that you have to print the answer modulo 998244353.

Solution in Python (3.8.2) (judge verdict: Wrong Answer)

import sys
sys.setrecursionlimit(10**7)

def input(): return sys.stdin.readline()[:-1]
mod = 10**9 + 7
mod2 = 998244353
def readInt():return int(input())
def readIntList():return list(map(int,input().split()))
def readStringList():return list(input())
def readStringListWithSpace():return list(input().split())
def readString():return input()

from itertools import accumulate
 
def execute():
    n,k = readIntList()
    s = set()
    for _ in range(k):
        l,r = readIntList()
        s.add(l)
        s.add(r)
    s = list(s)
    dp = [0]*(n+1)
    for i in s :
        dp[i] = 1
    # dp[0] = 1
    for val in range(1,n+1):
        for coin in s:
            if val >= coin:
                dp[val] += dp[val-coin]
    print(dp[n-1]%mod2)

    


    
 
if __name__ == "__main__":
    execute()