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<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
#define N 200005
#define mod 998244353
#define rep(i, l, r) for(int i=l; i<=r; ++i)
using namespace std;
int t;
int n, k;
int l[11], r[11];
int f[N], s[N];
int main(){
	scanf("%d%d", &n, &k);
	rep(i, 1, k){
		scanf("%d%d", &l[i], &r[i]);
	}
	s[1]=f[1]=1;
	rep(i, 2, n){
		rep(j, 1, k){
			if(i>l[j]){
				if(i>r[j]) f[i]=((f[i]+s[i-l[j]]-s[i-r[j]-1])%mod+mod)%mod;
				else f[i]=(f[i]+s[i-l[j]])%mod;
			} 
		}
		//printf("%d %d\n", i, f[i]);
		s[i]=(s[i-1]+f[i])%mod;
	}
	printf("%d", f[n]);
	return 0;
}