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: Time Limit Exceeded)

import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int K = sc.nextInt();
		int dp[] = new int[N+1];
		int root[] = new int[N+1];
		Range ran[] = new Range[K];
		Main main = new Main();
		for (int i=0;i<K;i++) {
			Range r= main.new Range();
			r.start= sc.nextInt();
			r.end= sc.nextInt();
			ran[i] = r;
		}
		Arrays.sort(ran);
		dp[1]=1;
		for (int i=1;i<N;i++) {
			if (dp[i]==0) {
				continue;
			}
			for (int j=0;j<K;j++) {
				for (int k=ran[j].start;k<=ran[j].end;k++) {
					if (i+k>N) {
						break;
					}
					dp[i+k] = (dp[i+k]+dp[i])%998244353;
				}
			}
		}
		System.out.println(dp[N]);
	}

	public class Range implements Comparable{
		int start ;
		int end;
		@Override
		public int compareTo(Object o) {
			Range ran  = (Range)o;
			if (this.start<ran.start) {
				return -1;
			}
			return 1;
		}
	}
}