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>
#define mod 998244353
#define max_n 200000
#define max_k 10
using namespace std;
int /*dp[max_n+1],*/sum[max_n+1];
struct node{
	int l,r;
};
node a[max_k+1];
typedef const int& ci;
int cnt(int l,ci r){
	if(r<=0)
		return 0;
	l<=0&&(l=1);
	return sum[r]-sum[l-1]+mod;
}
int main(){
	int n,k;
	scanf("%d%d",&n,&k);
	for(int i=0; ++i<=k; scanf("%d%d",&a[i].l,&a[i].r));
	sum[1]=1,sum[0]=0;
	long long num;
	for(int i=1; ++i<=n; sum[i]=(sum[i-1]+num)%mod)
		for(int j=num=0; ++j<=k; num+=cnt(i-a[j].r,i-a[j].l));
	num=sum[n]-sum[n-1];
	printf("%lld\n",num<0?(num+mod):num);
	return 0;
}