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 <algorithm>
using namespace std;
#define Nmax 200010
#define GETMD(a) ((a)%998244353+998244353)%998244353
#define MD 998244353
int N;
int K;
int sg[13][2];
long long sm[Nmax];
long long F[Nmax];
int main()
{
	scanf("%d %d", &N, &K);
	for (int i = 0; i < K; i++)
	{
		scanf("%d %d", &sg[i][0], &sg[i][1]);
	}
	F[1] = 1;
	sm[1] = 1;
	for (int i = 2; i <= N; i++)
	{
		F[i] = 0;
		for (int j = 0; j < K; j++)
		{
			F[i] = GETMD(F[i] + sm[max(i-sg[j][0], 0)] - sm[max(0, i-sg[j][1]-1)]);
		}
		sm[i] = GETMD(sm[i-1] + F[i]);
	}
	printf("%lld\n", F[N]);
	
	return 0;
}