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<iostream>
using namespace std;
const long mod=998244353;
int N,K;
int L[10],R[10];
long dp[2<<17];
int main()
{
	cin>>N>>K;
	for(int i=0;i<K;i++)cin>>L[i]>>R[i];
	dp[0]=1;
	dp[1]=-1;
	for(int i=0;i<N;i++)
	{
		long now=dp[i]=(dp[i]%mod+mod)%mod;
		dp[i+1]+=now;
		for(int j=0;j<K;j++)
		{
			if(i+L[j]<N)dp[i+L[j]]+=now;
			if(i+R[j]+1<N)dp[i+R[j]+1]-=now;
		}
	}
	cout<<dp[N-1]<<endl;
}