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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
using P = pair<int, int>;
#define LARGE 1000000007

int main() {
	int n, k;
	cin >> n >> k;

	vector<int> l(11);
	vector<int> r(11);

	rep(i, k) cin >> l[i] >> r[i];

	vector<int> t(200005);
	int cnt = 0;
	rep(i, k) {
		rep(j, (r[i] - l[i]+1)) {
			t[cnt] = l[i] + j;
			cnt++;
		}
	}

//	cout << "data = ";
//	rep(i, cnt) cout << t[i] << ' ';
//	cout << endl;

	vector<int>dp(400005);
	dp[0]  =1;
	for(int i=0; i<n; i++) {
		if (dp[i] != 0) {
			for(int j=0; j<cnt; j++) {
				if ((i + cnt) > n) break;
				dp[i + t[j]] += dp[i];
				dp[i + t[j]] %= 998244353;
			}
		}
	}
//	cout << "dp = ";
//	rep(i, n) cout << dp[i] << ' ';
//	cout << endl;

	cout << dp[n-1] << endl;
	return 0;
}