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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.util.*;
public class Main {
	static int N;
	static int K;
	
	static int[]S;
	
	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner sc= new Scanner(System.in);
		N= sc.nextInt();
		K= sc.nextInt();
		
		S= new int[N+1];
		
		Arrays.fill(S, -1);
		
		for(int i=0;i<K;i++){
			int l= sc.nextInt();
			int r= sc.nextInt();
			
			for(int j= l;j<=r;j++)S[j]= 1;
			
		}
		
		sc.close();
		
		
		int ans= solve(1,1,0);
		
		System.out.println(ans);
		
		
	}
	static int solve(int i,int d,int cnt){
		if( i == N) return kaijou(cnt);
		if(i > N)return 0;
		
		int nextd= next(d);
		
		int res1= solve(i+ nextd, nextd, cnt++);
		int res2= solve(i, d, cnt);
		
		return res1+ res2;

	}
	
	static int next(int d){
		int res= d+1;
		
		while(res < N){
			if(S[res] == 1)return res;
			res++;
		}
		return N;
	}
	
	static int kaijou(int n){
		int res= 1;
		
		for(int i=n;i>0;i--)res *= n;
		
		return res;
		
	}

}