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: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author silviase
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DLeapingTak solver = new DLeapingTak();
        solver.solve(1, in, out);
        out.close();
    }

    static class DLeapingTak {
        long[] dp_acc;
        static long MOD = 998244353;

        public void solve(int testNumber, Scanner in, PrintWriter out) {

            int n = in.nextInt();
            int k = in.nextInt();
            int[] l = new int[k];
            int[] r = new int[k];
            for (int i = 0; i < k; i++) {
                l[i] = in.nextInt();
                r[i] = in.nextInt();
            }

            long[] dp = new long[n];
            dp_acc = new long[n];
            for (int i = 0; i < n; i++) {
                dp_acc[i] = i == 0 ? 1 : 0;
            }

            for (int i = 1; i < n; i++) {
                for (int j = 0; j < k; j++) {
                    dp[i] += dp_acc(i - r[j], i - l[j]);
                  	dp[i] %= MOD;
                    dp_acc[i] = (dp_acc[i - 1] + dp[i]) % MOD;
                }
            }

            System.out.println(dp[n - 1] % MOD);

        }

        public long dp_acc(int l, int r) {
            long left, right;
            if (l <= 0) {
                left = 0;
            } else {
                left = dp_acc[l - 1];
            }

            if (r < 0) {
                right = 0;
            } else {
                right = dp_acc[r];
            }

            return (right - left) % MOD;
        }

    }
}