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 C (GCC 9.2.1) (judge verdict: Runtime Error)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<stdbool.h>
#include<math.h>
#include<limits.h>
#define MAX 20002
#define MOD 998244353

typedef long long ll;

int max(int a,int b){
    if(a>b) return a;
    else return b;
}

int min(int a,int b){
    if(a<b) return a;
    else return b;
}

/*qsort(array,num_of_index,sizeof(int),compare_int); */
 int compare_int(const void *a,const void *b){
     return *(int*) a - *(int *) b; 
 } 
 
int main(){
    ll N,K;
    scanf("%lld %lld",&N,&K);
    ll L[12],R[12];
    ll num[MAX]={0};
    for(ll i=1;i<=K;i++){
        scanf("%lld %lld",L+i,R+i);
        for(ll j=L[i];j<=R[i];j++){
            num[j] = 1;

        }
    }
    ll step[MAX],step_num=0;
    for(ll i=1;i<MAX;i++){
        if(num[i] == 1)
            step[step_num++] = i;
    }
    ll DP[MAX] = {0};
    DP[1] = 1;
    for(ll i=2;i<=N;i++){
        ll j=0;
        while(i - step[j] >= 1 && j < step_num){
            DP[i] += DP[i-step[j]];
            DP[i] %= MOD;
            j++;
        }
    }
    printf("%lld",DP[N]);
}