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 C# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
    const int Mod = 998244353;

    public static void Main()
    {
        var nk = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
        var (n, k) = (nk[0], nk[1]);
        var lengthSum = 0;
        var segments = new (int L, int R)[k];
        for (int i = 0; i < segments.Length; ++i)
        {
            var s = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            segments[i] = (s[0], s[1]);
            lengthSum += s[1] - s[0] + 1;
        }

        Array.Sort(segments);

        var ds = new List<int>(lengthSum);
        for (int i = 0; i < segments.Length; ++i)
        {
            var (offset, length) = new Range(segments[i].L, segments[i].R + 1).GetOffsetAndLength(n + 1);
            ds.AddRange(E.Range(offset, length));
        }

        var dp = new int[n];
        dp[0] = 1;
        for (int i = 1; i < dp.Length; ++i)
        {
            for (int j = 0; j < ds.Count; ++j)
            {
                if (ds[j] > i)
                {
                    break;
                }

                dp[i] += dp[i - ds[j]]; dp[i] %= Mod;
            }
        }

        Console.WriteLine(dp[n - 1]);
    }
}