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,x,y) for(int i=x,i##end=y;i<=i##end;++i)
#define _rep(i,x,y) for(int i=x,i##end=y;i>=i##end;--i)
#define ll long long
#define N 1000005
const int mod=998244353;
inline void reduce(int&x){x-=mod,x+=x>>31&mod;}
int dp[N],sum[N],n,k,L[N],R[N];
int main(){
	std::ios::sync_with_stdio(0);
	std::cin>>n>>k;
	rep(i,1,k) std::cin>>L[i]>>R[i];
	dp[1]=sum[1]=1;
	rep(i,2,n){
		rep(j,1,k){
			if(i-L[j]<=0) continue;
			int l=std::max(1,i-R[j]),r=i-L[j];
			reduce(dp[i]+=sum[r]);
			reduce(dp[i]+=mod-sum[l-1]);
		}
		sum[i]=sum[i-1];
		reduce(sum[i]+=dp[i]);
	}
	std::cout<<dp[n]<<'\n';
	return 0;
}