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 rep(i,n) for(int i=0; i<(int)(n); i++)

using namespace std;
using LL = long long;
using P = pair<int,int>;
const LL mod = 998244353;

int main(){
	LL N, K;
	cin >> N >> K;
	vector<LL> L(K), R(K);
	rep(i,K) cin >> L[i] >> R[i];
	vector<LL> dp(N+1), num(K), sum(N+1);
	dp[1]=1, sum[1]=1;
	for(int i=2; i<=N; i++){
		rep(j,K){
			if(R[j]<i){
				num[j]+=dp[i-L[j]];
				num[j]-=dp[i-R[j]-1];
				dp[i]+=num[j];
			}
			else if(L[j]<i){
				num[j]+=dp[i-L[j]];
				dp[i]+=sum[i-L[j]];
			}
			dp[i]%=mod;
			sum[i]=(sum[i-1]+dp[i]);
			sum[i]%=mod;
		}
	}
	LL ans=dp[N];
	while(ans<0) ans+=mod;
	cout << ans << endl;

	return 0;
}