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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    public class Program
    {
        const int Mod = 998244353;
        public static void Main (string[] args)
        {
            new Program ().Solve (new ConsoleInput (Console.In, ' '));
        }

        public void Solve (ConsoleInput cin)
        {
            int N = cin.ReadInt;
            int K = cin.ReadInt;

            int l, r;
            List<int> S = new List<int>();

            for(int i = 0;i<K;i++){
                l = cin.ReadInt;
                r = cin.ReadInt;

                for(int j=l;j<=r;j++) S.Add(j);
            }

            long[] dp = new long[N];
            dp[0] = 1;
            for(int i=1;i<N;i++){
                foreach(int j in S){
                    if(i-j>=0) dp[i] += dp[i-j] % Mod;
                }
                dp[i] = dp[i] % Mod;
            }

            Console.WriteLine(dp[N-1]);

        }

        public static long CombinationMod (long m, long n)
        {
            var a = 1L;
            var b = 1L;
            for (long i = 1; i <= n; i++)
            {
                a = (a * (m - i + 1)) % Mod;
                b = (b * i) % Mod;
            }

            return ModDiv (a, b) % Mod;
        }
        static long ModDiv (long x1, long x2)
        {
            long bb = ModPow (x2, Mod - 2);
            return (x1 * bb) % Mod;
        }

        static long ModPow (long x1, long x2)
        {
            long ans = 1;
            while (x2 > 0)
            {
                if (x2 % 2 == 1)
                {
                    ans = (ans * x1) % Mod;
                }
                x2 /= 2;
                if (x2 == 0) break;
                x1 = (x1 * x1) % Mod;
            }
            return ans % Mod;
        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput (System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string> ();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue ();
                string[] tmp = _stream.ReadLine ().Split (_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue (tmp[i]);
                return inputStream.Dequeue ();
            }
        }
        public string ReadLine { get { return _stream.ReadLine (); } }
        public int ReadInt { get { return int.Parse (Read); } }
        public long ReadLong { get { return long.Parse (Read); } }
        public double ReadDouble { get { return double.Parse (Read); } }
        public string[] ReadStrArray (long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray (long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray (long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }
}