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;

int main() {
	long long n,k,i,j,mod=998244353;
	cin >> n >> k;
	
	vector<pair<long,long>> d(k);
	for(j=0; j<k; j++){
		cin >> d[j].first >> d[j].second;
	}
	
	vector<long long> ans(n+1+100000,0),cur(n+1+100000,0);
	long long l,r,res;
	
	res=1;
	for(i=1; i<n; i++){
		for(j=0; j<k; j++){
			l=d[j].first; r=d[j].second+1;
			if(i+l>n){
				l=n+1-i;
			}
			if(i+r>n){
				r=n+1-i;
			}
			cur[i+l]+=res; cur[i+r]-=res;
		}
		ans[i+1]=(ans[i]+cur[i+1])%mod;
		res=(ans[i]+cur[i+1])%mod;
	}
	
	ans[n]%=mod;
	if(ans[n]<0){
		ans[n]+=mod;
	}
	cout << ans[n] << endl;
	return 0;
}