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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
    final int mod = 998244353;
    int[] tree;

    private void add(int num, int from, int to, int a, int b, int node) {
        if (from <= a && b <= to) {
            tree[node] += num;
            tree[node] %= mod;
            return;
        }

        int mid = (a + b) / 2;
        if (from <= mid) add(num, from, to, a, mid, node * 2);
        if (to > mid) add(num, from, to, mid + 1, b, node * 2 + 1);
    }

    private int getSum(int index, int a, int b, int node) {
        if (a == b) return tree[node];

        int mid = (a + b) / 2;
        int sum = 0;
        if (index <= mid) sum += getSum(index, a, mid, node * 2);
        if (index > mid) sum += getSum(index, mid + 1, b ,node * 2 + 1);

        sum += tree[node];
        sum %= mod;

        return sum;
    }

    public static void main(String[] args) throws IOException {
        new Main().solve();
    }

    private void solve() throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        StringTokenizer tokenizer = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(tokenizer.nextToken());
        int k = Integer.parseInt(tokenizer.nextToken());
        int[][] intervals = new int[k][2];
        for (int i = 0; i < k; i++) {
            tokenizer = new StringTokenizer(f.readLine());
            intervals[i][0] = Integer.parseInt(tokenizer.nextToken());
            intervals[i][1] = Integer.parseInt(tokenizer.nextToken());
        }

        tree = new int[4 * n];
        add(1, 0, 0, 0, n - 1, 1);

        for (int i = 0; i < n; i++) {
            for (int[] interval : intervals) {
                if (i + interval[0] >= n) continue;
                add(getSum(i, 0, n - 1, 1), i + interval[0], Math.min(i + interval[1], n - 1), 0, n - 1, 1);
            }
        }

        out.println(getSum(n - 1, 0, n - 1, 1));

        out.close();
    }
}