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: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
    
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new java.io.InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(br.readLine());

        int N = Integer.parseInt(st.nextToken());
        int K = Integer.parseInt(st.nextToken());

        long cut = 998244353;

        int[] l_array = new int[K];
        int[] r_array = new int[K];

        for(int i = 0; i < K; i++) {
            String[] input_array = br.readLine().split(" ");
            l_array[i] = Integer.parseInt(input_array[0]);
            r_array[i] = Integer.parseInt(input_array[1]);
        }
        
        long[] dp = new long[N + 10];
        dp[1] = 1;

        long[] sum_array = new long[N + 10];
        sum_array[1] = 1;

        for(int i = 2; i <= N; i++) {    
            
            for(int j = 0; j < K; j++) {
                int max_index = i - l_array[j];
                int min_index = i - r_array[j];

                if(min_index <= 0 && max_index <= 0) {
                    continue;
                } else if(min_index <= 0 && max_index > 0) {
                    min_index = 1;
                }

                long sum = sum_array[max_index] - sum_array[min_index - 1];

                if(sum < 0) sum += cut;

                dp[i] += sum;
                dp[i] %= cut;
            }

            sum_array[i] = (sum_array[i-1] + dp[i]) % cut;

        }
        
        pw.println(dp[N]);
        br.close();
        pw.close();
    }
}