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>
#define rei register int
#define int long long
using namespace std;
const int maxn = 200010,mod = 998244353;
int n,k;
int l[maxn],r[maxn];
int sum[maxn],dp[maxn];
void add(int &x,int y){
	x = x + y < mod ? x + y : x + y - mod;
}
signed main(){
	cin >> n >> k;
	for(rei i = 1;i <= k;++i) scanf("%lld%lld",&l[i],&r[i]);
	dp[1] = sum[1] = 1;
	for(rei i = 2;i <= n;++i){
		for(rei j = 1;j <= k;++j){
			add(dp[i],(sum[max(i - l[j],(long long)0)] - sum[max(i - r[j],(long long)1) - 1] + mod) % mod);
		} add(sum[i],sum[i - 1]),add(sum[i],dp[i]);
	} cout << dp[n] << endl; return 0;
}