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;
#define make_pair(a, b) mp(a, b)
typedef pair<int, int> pii; 
typedef long long ll;
const int maxn = 2e5 + 10;
const ll mod = 998244353;
ll f[maxn], g[maxn];
int n, k, l[20], r[20];
ll sum(int x) { return x > n ? 0 : g[x];}
int main()
{
	scanf("%d%d", &n, &k);
	for(int i = 1; i <= k; ++i) scanf("%d%d", &l[i], &r[i]);
	f[n] = 1; 
	g[n] = f[n];
	for(int i = n - 1; i; --i)
	{
		for(int j = 1; j <= k; ++j)
			f[i] = (f[i] + sum(i + l[j]) + mod - sum(i + r[j] + 1)) % mod;
		g[i] = (g[i + 1] + f[i]) % mod;
	}
	printf("%lld\n", f[1]);
	return 0;
}