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 {

	static long mod = 998244353;

	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in)) {
			int N = sc.nextInt();
			int K = sc.nextInt();
			Pair[] pairs = new Pair[K];
			for (int i = 0; i < K; i++) {
				int from = sc.nextInt();
				int to = sc.nextInt();
				pairs[i] = new Pair(from, to);
			}
			Arrays.sort(pairs);
			int idx = K;
			long[] arr = new long[N + 1];
			arr[1] = 1;
			for (int i = 1; i < N; i++) {
				if (i != 1 && arr[i] == 0) {
					continue;
				}

				for (int j = 0; j < idx; j++) {
					int from = pairs[j].x;
					if (i + from > N) {
						idx = j;
						break;
					}
					int to = pairs[j].y;
					for (int k = from; k <= to; k++) {
						if (i + k > N) {
							pairs[j].y = k - 1;
							break;
						} else {
							arr[i + k] = (arr[i] + arr[i + k]) % mod;
						}
					}
				}
			}
			System.out.println(arr[N]);
		}
	}

	static class Pair implements Comparable {
		int x;
		int y;

		public Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(Object x) {
			Pair other = (Pair) x;
			return this.x > other.x ? 1 : -1;
		}
	}
}