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.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;
using System.Numerics;

namespace abc179
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            if (File.Exists("input.txt"))
            {
                Console.SetIn(new StreamReader("input.txt"));
            }
            solve_abc179D();
            Console.Out.Flush();
        }

        public static void solve_abc179D()
        {
            int[] nk = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            int n = nk[0];
            int k = nk[1];
            int mod = 998244353;
            List<int> steps = new List<int>();
            while (k-- > 0)
            {
                int[] lr = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
                for (int i = lr[0]; i <= lr[1]; i++)
                {
                    steps.Add(i);
                }
            }
            steps.Sort();
            int[] dp = new int[n + 1];
            dp[0] = 1;
            for (int i = 1; i < n; i++)
            {
                for (int j = 0; j < steps.Count; j++)
                {
                    if (i - steps[j] >= 0)
                    {
                        dp[i] = (dp[i] % mod)  + (dp[i - steps[j]] % mod);
                    }
                    else
                    {
                        break;
                    }
                }
            }
            Console.WriteLine(dp[n - 1] % mod);
        }

        public static void solve_abc179C()
        {
            int n = Convert.ToInt32(Console.ReadLine());
            int cnt = 0;
            for (int i = 1; i <= 1000000; i++)
            {
                for (int j = 1; j <= 1000000; j++)
                {
                    if (i * j < n)
                    {
                        cnt++;
                        //Console.WriteLine("{0} * {1} = {2}, {3} - {2} = {4}", i, j, i * j, n, n - (i * j));
                    }
                    else
                    {
                        break;
                    }
                }
            }
            Console.WriteLine(cnt);
        }

        public static void solve_abc179B()
        {
            int t = Convert.ToInt32(Console.ReadLine());
            int cnt = 0;
            int max = 0;
            while (t-- > 0)
            {
                int[] d = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
                if (d[0] == d[1])
                {
                    cnt++;
                }
                else
                {
                    cnt = 0;
                }
                max = Math.Max(max, cnt);
            }
            Console.WriteLine(max >= 3 ? "Yes" : "No");
        }

        public static void solve_abc179A()
        {
            string s = Console.ReadLine();
            Console.WriteLine(s.EndsWith('s') ? s + "es" : s + "s");
        }
    }
}