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>
using namespace std;
typedef long long ll;
const int mod = 998244353;
int N, K;
vector<int> L, R;
int main() {
	cin >> N >> K;
	L.resize(K);
	R.resize(K);
	for (int i = 0; i < K; ++ i) {
		cin >> L[i] >> R[i];
	}
	vector<ll> hoge(N);
	hoge[0] = 1;
	hoge[1] = mod-1;
	ll s = 0;
	for (int i = 0; i < N; ++ i) {
		(s += hoge[i]) %= mod;
		for (int j = 0; j < K; ++ j) {
			int x = i + L[j];
			int y = i + R[j] + 1;
			if (x < N) (hoge[x] += s) %= mod;
			if (y < N) (hoge[y] += mod - s) %= mod;
		}
	}
	cout << s << endl;
}