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.*;

public class Main {
  static Scanner in = new Scanner(System.in);
  static List<Integer> list = new ArrayList<>();
  static int[] dp;
  static int n;
  static int m;
  static final long mod = 998244353;
  public static void main(String[] args) {
    n = in.nextInt();
    m = in.nextInt();
    list.clear();
    int le, ri;
    while (m-- > 0) {
      le = in.nextInt();
      ri = in.nextInt();
      for (int i = le; i <= ri; i++) {
        list.add(i);
      }
    }
    list.sort((a, b) -> a - b);
    dp = new int[n + 1];
    Arrays.fill(dp, 0);
    dp[1] = 1;
    for (int i = 1; i < n; i++) {
      if (dp[i] == 0) {
        continue;
      }
      for (int v : list) {
        if (v + i > n) {
          break;
        }
        dp[i + v] = (dp[i + v]  + dp[i]);
        if (dp[i + v] >= mod) {
          dp[i + v] %= mod;
        }
      }
    }
    System.out.println(dp[n]);
  }
}