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;

const long long MOD=998244353;
long long N,K,l[11],r[11],memo[200010],prefix[400010];

void Input(){
	cin>>N>>K;
	for(long long i=1; i<=K; i++){
		cin>>l[i]>>r[i];
	}
}

void Solve(){
	memset(prefix,0,sizeof prefix);
	prefix[N]=1; memo[N]=1;
	for(long long i=N-1; i>=1; i--){
		long long total=0;
		for(long long j=1; j<=K; j++){
			long long nl=l[j],nr=r[j];
			total+=(prefix[i+nl]-prefix[i+nr+1]+MOD)%MOD;
			total=total%MOD;
		}
		memo[i]=total;
		prefix[i]=(prefix[i+1]+total)%MOD;
	}
	cout<<memo[1]<<'\n';
}

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	Input();
	Solve();
}