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;
#define ll long long int
ll mod=998244353;
int main()
{
	ll i,j,k,m,n,t;
	cin>>n>>k;
	vector<pair<ll,ll>> v;
	for(i=0;i<k;i++)
	{
		ll  k1;
		cin>>j>>k1;
		v.push_back({j,k1});
	}
	ll ar[n],p[n];
	memset(ar,0,sizeof(ar));
	memset(p,0,sizeof(p));
	ar[0]=1;
	p[0]=1;
	for(i=1;i<n;i++)
	{
		for(auto x:v)
		{
			ll l=i-x.second;
			ll r=i-x.first;
			if(l<0 and r<0) continue;
			if(l<=0)
			ar[i]+=p[r];
			else
			{
				ll q=p[r]-p[l-1];
				if(q<0)
				q+=mod;
				else q%=mod;
				ar[i]+=q;
			}
			ar[i]%=mod;
		}
		p[i]=(p[i-1]+ar[i]%mod)%mod;
	}
	cout<<ar[n-1];
}