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;
#define INF 1LL<<62
#define inf 998244353
ll ans[500010]={};
int main() {
	ll n,k;
	cin>>n>>k;
	ans[1]=1;
	ll l[12],r[12];
	for(ll i=0;i<k;i++){
		cin>>l[i]>>r[i];
		r[i]++;
	}
	ll cnt=0;
	for(ll i=1;i<=n;i++){
		cnt+=ans[i];
		cnt%=inf;
		if(cnt<0){
			cnt+=inf;
		}
		for(ll j=0;j<k;j++){
			ans[i+l[j]]+=cnt;
			ans[i+l[j]]%=inf;
			ans[i+r[j]]-=cnt;
			if(ans[i+r[j]]<0){
				ans[i+r[j]]+=inf;
			}
		}
	}
	cout << ans[n];
	// your code goes here
	return 0;
}