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<bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;

const long long INF=INT_MAX/4;
const long long MOD=998244353;
const double EPS=1e-14;
const bool DEBUG=false;

const string YES = "YES";
const string NO = "NO";
const string Yes = "Yes";
const string No = "No";

template<class T>
void debug(T head){
    if(DEBUG){
        cout<<head<<endl;
    }
}

template <class Head, class... Body>
void debug(Head head, Body... body){
    if(DEBUG){
        cout<<head<<" ";
        debug(body...);
    }
}

/////
void answer(){
    long N, K;
    cin>>N>>K;
    vector<unsigned long long> L(K), R(K);
    vector<unsigned long long> dp(N, 0), csum(N, 0);
    for(int i=0; i<K; ++i){
        cin>>L[i]>>R[i];
    }

    dp[0] = 1;
    csum[0] = dp[0];
    for(int i=1; i<N; ++i){
        for(int j=0; j<K; ++j){
            dp[i] += csum[max(0ull, i-L[j])] - csum[max(0ull, i-R[j]-1)] + MOD;
            dp[i] %= MOD;
        }
        dp[i] %= MOD;
        debug(dp[i]);
        csum[i] = (csum[i-1] + dp[i]) % MOD;
    }

    cout<<dp[N-1]<<endl;

    return;
}

/////

int main(int argc, char* argv[]){
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout.precision(16);

    answer();

    return 0;
}