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 <iostream>
using namespace std;

const int mod=998244353;
int n,k,sum[500005],L[200005],R[200005];

void add(int x,int c) {
	if (c<0) c=(c+mod)%mod;
	for (;x<=n;x+=x&-x) sum[x]=(sum[x]+c)%mod;
}

int que(int x) {
	int ret=0;
	for (;x>=1;x-=x&-x) ret=(ret+sum[x])%mod;
	return ret;
}

int main()
{
	scanf("%d%d",&n,&k);
	for (int i=1;i<=k;i++) {
		scanf("%d%d",&L[i],&R[i]);
	}
	sum[1]=1;
	for (int i=1;i<=n;i++) {
		for (int j=1;j<=k;j++) {
			if (i+L[j]<=n) add(i+L[j],que(i));
			add(min(n+1,i+R[j]+1),-que(i));
		}
	}
	printf("%d\n",que(n));
	
	return 0;
}