Problem: 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.

Examples

Input

5 2
1 1
3 4


Output

4


Input

5 2
3 3
5 5


Output

0


Input

5 1
1 2


Output

5


Input

60 3
5 8
1 3
10 15


Output

221823067

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define Int int64_t

using namespace std;

int main() {
	constexpr Int MOD = 998244353;
	int N, K;
	cin >> N >> K;
	vector<int> L(K), R(K);
	for (int i = 0; i < K; ++i) {
		cin >> L[i] >> R[i];
	}

	vector<Int> d(N + 10, 0);
	vector<Int> a(N + 10, 0);
	a[1] = 1;
	for (int i = 1; i <= N; ++i) {
		(d[i] += d[i - 1]) %= MOD;
		(a[i] += d[i]) % MOD;
		for (int k = 0; k < K; ++k) {
			if (i + L[k] > N) { continue; }
			int r = min(N, i + R[k]) + 1;
			(d[i + L[k]] += a[i]) %= MOD;
			(d[r] += MOD - a[i]) %= MOD;
		}
	}
	cout << a[N] % MOD << "\n";

	return 0;
}