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 ll mod = 998244353;

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	int n,k;
	cin>>n>>k;
	vector<pair<int,int>>s;
	vector<int>dp(2*n+5);

	for(int i=0;i<k;i++){
		int l,r;
		cin>>l>>r;
		s.push_back({l,r});
	}
	
	/*
	for(int j:s){
		cout<<j<<' ';
	}
	cout<<'\n';
	*/
	dp[1]=1;
	for(int i=1;i<=n;i++){
		dp[i]=(dp[i-1]+dp[i])%mod;
		for(int j=0;j<k;j++){
			int l = s[j].first,r=s[j].second;

			dp[i+l]=(dp[i]+dp[i+l])%mod;
			dp[i+r+1]=(dp[i+r+1]-dp[i])%mod;
		}
	}
	ll ans=(dp[n]-dp[n-1]+mod)%mod;
	cout<<ans<<'\n';
	
	return 0;
}