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)

//Created by Aminul on 9/19/2020.

import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    static final long mod = 998244353;

    public static void main(String[] args) throws Exception {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = in.nextInt();
        int k = in.nextInt();
        int ranges[][] = new int[n][2];
        for (int i = 0; i < k; i++) {
            ranges[i][0] = in.nextInt();
            ranges[i][1] = in.nextInt();
        }
        Arrays.sort(ranges, (x, y) -> {
            int cmp = Integer.compare(x[0], y[0]);
            if (cmp == 0) cmp = Integer.compare(x[1], y[1]);
            return cmp;
        });

        BinaryIndexTree bit = new BinaryIndexTree(n + 5);
        for (int i = n; i >= 1; i--) {
            if (i == n) {
                bit.add(i, 1);
            } else {
                long ways = 0;
                for (int range[] : ranges) {
                    int l = i + range[0], r = i + range[1];
                    if(l > n) break;
                    r = min(r, n);
                    ways += bit.query(l, r);
                    if (ways >= mod) {
                        ways -= mod;
                    }
                    if (r >= n) break;
                }
                bit.add(i, ways);
            }
        }

        pw.println(bit.query(1, 1));

        pw.close();
    }

    static class BinaryIndexTree {
        public long bit[];
        public int n;

        public BinaryIndexTree(int N) {
            n = N;
            bit = new long[n];
        }

        public void add(int index, long value) {
            for (; index < n; index = index + (index & -index)) {
                bit[index] += value;
                if (bit[index] >= mod) bit[index] -= mod;
            }
        }

        public long sum(int index) {
            long sum = 0;
            for (; index > 0; index = index - (index & -index)) {
                sum += bit[index];
                if (sum >= mod) sum -= mod;
            }
            return sum;
        }

        public long query(int i, int j) {
            long res = sum(j) - sum(i - 1);
            //res %= mod;
            if (res < 0) res += mod;
            return res;
        }
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
    
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
    
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }
    
        public String next() throws Exception {
            while (tokenizer == null || !tokenizer.hasMoreTokens())
                tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }
    
        public String nextLine() throws Exception {
            String line = null;
            tokenizer = null;
            line = reader.readLine();
            return line;
        }
    
        public int nextInt() throws Exception {
            return Integer.parseInt(next());
        }
    
        public double nextDouble() throws Exception {
            return Double.parseDouble(next());
        }
    
        public long nextLong() throws Exception {
            return Long.parseLong(next());
        }
    
    }
}