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 <iomanip>
#include <cstdio>
#include <fstream>
#include <cmath>
#include <algorithm>
#include <string>
#include <cstring>
#include <vector>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <stack>
#include <queue>
#include <deque>
#include <bitset>
//MACROS
#define _crt_secure_no_warnings
#define FREEELO ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define pb push_back
#define mp make_pair
#define INF 0x3F3F3F3F
#define MAX 200001
#define MOD 998244353
#define ALPHABET 128
#define loop(i, n) for (int i = 1; i <= (n); i++)
#define loop0(i, n) for (int i = 0; i < (n); i++)
#define sz(x) (int)x.size()
#define all(v) v.begin(), v.end()
#define F first
#define S second
using namespace std;
typedef long long ll;
typedef pair<ll, ll> llll;
typedef pair<int, int> ii;
typedef unordered_map<int, int> umii;
typedef unordered_map<ll, ll> umll;
typedef unordered_set<int> usi;
typedef unordered_multiset<int> usmi;
ll dp[MAX];
umii m;
int main() {
    FREEELO
    int n, k; cin >> n >> k;
    dp[1] = 1;
    vector<ii> steps(k + 1);
    loop(i, k){
        cin >> steps[i].F >> steps[i].S;
    }
    if (n == 1) { cout << 0; return 0; }
    for (int i = 2; i <= n; i++){
        for (int j = 0; j < sz(steps); j++){
            for (int k = steps[j].F; k <= steps[j].S; k++){
                if (i - k < 0) break;
                dp[i] = (dp[i] + dp[i - k]) % MOD;
            }
        }
    }
    cout << dp[n] << endl;

}