Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5 2
1 1
3 4

Sample Output 1

4

The set S is the union of the segment [1, 1] and the segment [3, 4], therefore S = \{ 1, 3, 4 \} holds.

There are 4 possible ways to get to Cell 5:

1 \to 2 \to 3 \to 4 \to 5,

1 \to 2 \to 5,

1 \to 4 \to 5 and

1 \to 5.

Sample Input 2

5 2
3 3
5 5

Sample Output 2

0

Because S = \{ 3, 5 \} holds, you cannot reach to Cell 5.
Print 0.

Sample Input 3

5 1
1 2

Sample Output 3

5

Sample Input 4

60 3
5 8
1 3
10 15

Sample Output 4

221823067

Note that you have to print the answer modulo 998244353.

Solution in C++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;

#define gcd(a,b)		__gcd(a,b)
#define lcm(a,b)		(a*b)/gcd(a,b)
#define ff              first
#define ss              second
#define int             long long
#define float			double
#define pb              emplace_back
#define mp              make_pair
#define pii             pair<int,int>
#define vi              vector<int>
#define vc				vector<char>
#define vb				vector<bool>
#define vf				vector<float>
#define vs				vector<string>
#define mii             map<int,int>
#define pqb             priority_queue<int>
#define pqs             priority_queue<int,vi,greater<int>>
#define hashmap         unordered_map
#define setbits(x)      __builtin_popcountll(x)
#define zrobits(x)      __builtin_ctzll(x)
#define mod             1000000007
#define inf             INT64_MAX
#define ps(x,y)         fixed<<setprecision(y)<<x
#define mk(arr,n,type)  type *arr=new type[n];
#define w(x)            int x; cin>>x; while(x--)
#define all(x)			x.begin(),x.end()
#define digits(x)		floor(log10(x))+1
#define FIO				ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)

template<class T>
void printV(vector<T> a) {for (auto v : a)cout << v << " ";}
template<class T>
void readV(vector<T>& a) {int n = a.size(); for (int i = 0 ; i < n ; i++)cin >> a[i];}
template<class T>
void printA(T* a , int n) {for (int i = 0; i < n  ; i++)cout << a[i] << " ";}
template<class T>
void readA(T* a , int n) {for (int i = 0 ; i < n ; i++)cin >> a[i];}
auto clk = clock();
mt19937_64 rang(chrono::high_resolution_clock::now().time_since_epoch().count());
void run_time() {cout << endl<<"Time elapsed: " << (double)(clock() - clk) / CLOCKS_PER_SEC << endl;}

void aryan_pandeya() {
#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
#endif
}
int M = 998244353;
int solve(int n , set<int> a){
	int dp[n] = {0};
	dp[0] = 1 ;
	for(int i = 1 ; i<n ; i++){
		for(auto v:a){
			if(i-v<0){
				continue;
			}
			else{
				dp[i]= (dp[i]+dp[i-v])%M;
			}
		}
	}
	return dp[n-1]%M;
}
 
int32_t main() {
	aryan_pandeya();
	FIO;


	int n , k ;
	cin>>n>>k ;
	set<int> s; 
	for(int i = 0 ; i<k ; i++){
		int x , y ;
		cin>>x>>y;
		for(int j = x ; j<=y ; j++){
			s.insert(j);
		}
	}
	// vi a;
	// while(!s.empty()){
	// 	a.pb(*s.begin());
	// 	s.erase(s.begin());
	// }
	// printV(a);
	// cout<<'\n';

	int ans = solve(n,s);
	cout<<ans;

	return 0;
}