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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back 
#define mp make_pair
#define f first
#define s second
#define sz(x) ((int)x.size())
const ll maxint=2e18;
const ll minint =-2e18;
/*******\
(͡ ° ͜ʖ ͡ °) : Hello there, relax.
\*     */
const int mod = 998244353;
int n;
const int M = 2e5+5;
ll done[M];
vector<pair<int,int>> edges;
ll solve(int position){
    if(position > n)return 0;
    if(position == n)return 1;
    if(done[position] != -1)return done[position];
    ll res = 0;
    for(auto i:edges){
        for(int start=i.f;start<=i.s;start++){
            res += solve(position+start);
            res%=mod;
        }
    }

    return done[position] = res%mod;
}

int main(){
    memset(done,-1,sizeof(done));
    int k;
    scanf("%d%d",&n,&k);
    edges.assign(k,pair<int,int>());
    for(int i=0;i<k;i++){
        scanf("%d%d",&edges[i].f,&edges[i].s);
    }
    sort(edges.begin(),edges.end());
    cout<<solve(1)%mod<<'\n';
    return 0;
}