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 <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <set>
#include <cmath>
#include <stdio.h>
#include <list>
#include <numeric>
#include <stack>
#include <queue>
#include <tuple>
#include <bitset>
#include <map>
#include <math.h>
//ceil(a/b)   (a + (b - 1))/ b
using namespace std;
#define rep(i,n) for(int i = 0; i < (n); i++)
typedef long long ll;
typedef pair<int,int> P;
const int inf=1000000007;
const ll mod=998244353;
const double PI=3.14159265358979323846;
int dx[] = {1,-1,0,0};
int dy[] = {0,0,1,-1};




ll sq[1000010];

int main(){
    int N,K;
    set<int> st;
    cin >> N >> K;
    rep(i,K) {
	int l,r;
	cin >> l >> r;
	for(int i=l; i<=r; i++) st.insert(i);
    }
    
    sq[1] = 1;
    for(int i=1; i<=N; i++) {
	for(auto itr : st) {
	    sq[i+itr] += sq[i];
	    sq[i] %= mod;
	}
    }
    
    cout << sq[N] << endl;
    

//    for(auto itr : st) cout << itr << endl;
    

    return 0;
}