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 <string>
#include <vector>
#include <algorithm>
#include <map>
#include <list>
#include <utility>
#include <tuple>
#include <cstdio>
#include <set>
#include <queue>
#include <stack>
#include <deque>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <cctype>
#include <cmath>
#include <limits>
#include <iomanip>
#define _GLIBCXX_DEBUG
#define rep(i,n) for(int i=0;i<(n);++i)
using namespace std;
const long long INF = 1LL << 60;
typedef long long ll;
int main() {
    const ll mod = 998244353;
    ll N,K;
    cin >> N >> K;
    //
    vector<ll>L(K);
    vector<ll>R(K);
    for(ll i=0;i<K;i++){
        cin >> L[i] >> R[i];
    }
    //
    sort(L.begin(), L.end() );
    sort(R.begin(), R.end() );
    //
    vector<ll> dp(N+1);
    dp[1]=1;
    
    //最大N回移動する
    for(int i=1;i<=N;i++){
        bool frg = false;
        for(int j=0;j<K;j++){
            for(int k=L[j];k<=R[j];k++){
                if((i+k) <= N){
                    dp[i+k] = dp[i+k] + dp[i];
                    if(dp[i+k]>mod){
                        dp[i+k]= dp[i+k] % mod;
                    }
                }
                else{
                    frg = true;
                    break;
                }
            }
            if(frg){
                break;
            }
        }
    }

    if(dp[N] >= mod){
        dp[N]=dp[N] % mod;
    }
    cout << dp[N] << endl;

}