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.Collections.Generic;
using System.Linq;

namespace AtCoderBiginnerContest179
{
	class Program
	{
		private static int MOD = 998244353;

		static void Main(string[] args)
		{
			var inputs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			var array = new int?[inputs[0]];
			array[0] = 1;

			var list = new List<int>();
			for (var i = 0; i < inputs[1]; i++)
			{
				var tmpInputs = Console.ReadLine().Split().Select(int.Parse).ToArray();
				list.AddRange(Enumerable.Range(tmpInputs[0], tmpInputs[1] - tmpInputs[0] + 1));
			}
			var set = list.OrderBy(x => x).ToArray();

			int CulcurateRoute(int n)
			{
				if (array[n] != null)
				{
					return array[n].Value;
				}

				if (n - set[0] < 0)
				{
					array[n] = 0;
					return 0;
				}

				var tmp = 0;
				for (var i = 0; i < set.Length; i++)
				{
					if (n - set[i] < 0)
					{
						break;
					}
					tmp += CulcurateRoute(n - set[i]);
					tmp %= MOD;
				}
				array[n] = tmp;
				return tmp;
			}


			Console.WriteLine(CulcurateRoute(inputs[0] - 1));
		}

	}
}