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;
typedef long long int ll;
typedef pair<ll,ll> P;
typedef vector<ll> VI;
typedef vector<VI> VVI;
const ll MOD = 998244353;
const ll INF = 1e18;
#define REP(i,n) for(int i=0;i<n;i++)
#define ALL(v) v.begin(),v.end()

int main(){
	int n, k; cin >> n >> k;
	VI l(k), r(k);
	REP(i,n) cin >> l[i] >> r[i];
	VI dp(n); dp[0]=1; dp[1]=-1;
	ll now=0;
	for(int i=0;i<n;i++){
		now=(now+dp[i])%MOD;
		REP(j,k){
			int lp=i+l[j], rp=i+r[j]+1;
			if(lp<n)
				dp[lp]=(dp[lp]+now)%MOD;
			if(rp<n)
				dp[rp]=(dp[rp]-now+MOD)%MOD;
		}
	}
	cout << now << endl;
	return 0;
}