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 l_ength size
const int inf = (1<<30);
const int mod = 998244353;
using ll = long long;
using namespace std;

ll dp[200100];
ll sum[200100];
vector<pair<int, int>> vspan;

int main(){
	int n, k; cin >> n >> k;
	for( int i = 0; i < k; ++i ){
		int x, y; cin >> x >> y;
		vspan.emplace_back(x, y);
	}
	dp[0] = 1;
	sum[1] = 1;
	for( int i = 0; i < n; ++i ){
		for( int s = 0; s < k; ++s ){
			int l = vspan[s].first;
			int r = vspan[s].second;
			dp[i+1] += ( mod + sum[max(0, i+2-l)]-sum[max(0, i+2-r-1)] );
			dp[i+1] %= mod;
		}
		sum[i+2] = sum[i+1] + dp[i+1];
		sum[i+2] %= mod;
	}
	cout << dp[n-1] % mod << endl;
}