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;
const int mod = 998244353;
int main() {
	int n, k; cin>>n>>k;
	vector<pair<int, int>> a(k);
	for(int i = 0; i < n; i++){
		cin>>a[i].first>>a[i].second;
	}
	vector<int> dp(n), pref(n);
	dp[0] = pref[0] = 1;
	for(int i = 1; i < n; i++){
		for(pair<int, int> p: a){
			int l = max(0, i - p.second);
			int r = i - p.first;
			if(l <= r){
				dp[i] += pref[r];
				if(l >= 1) dp[i] -= pref[l-1];
				dp[i] %= mod;
				if(dp[i] < 0) dp[i] += mod;
			}
		}
		pref[i] = (pref[i - 1] + dp[i]) % mod;
	}
	cout<<dp[n - 1]<<endl;
}