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

public class HelloWorld
{
    static bool res = false;
    static List<long> avail;
    static long[] memo;
    static public void Main()
    {
        var NK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var N = NK[0];
        var K = NK[1];

        avail = new List<long>();
        memo = new long[N + 1];
        memo[1] = 1;
        for (int i = 0; i < K; i++)
        {
            var LR = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            for (int j = LR[0]; j <= LR[1]; j++)
            {
                avail.Add(j);
            }
        }


        Console.WriteLine(Check(N).value);
    }

    static Modular Check(long N)
    {
        if (memo[N] > 0) return memo[N];
        var res = new Modular(0);
        foreach (var item in avail)
        {
            if(N - item>= 1)
            {
                res += Check(N - item);
            }
        }

        memo[N] = res.value;
        return memo[N];
    }
}

class Modular
{
    private const int M = 998244353;
    public long value;
    public Modular(long value) { this.value = value; }
    public static implicit operator Modular(long a)
    {
        var m = a % M;
        return new Modular((m < 0) ? m + M : m);
    }
    public static Modular operator +(Modular a, Modular b)
    {
        return (a.value + b.value) % M;
    }
    public static Modular operator -(Modular a, Modular b)
    {
        return a.value - b.value;
    }
    public static Modular operator *(Modular a, Modular b)
    {
        return a.value * b.value;
    }
    public static Modular Pow(Modular a, int n)
    {
        switch (n)
        {
            case 0:
                return 1;
            case 1:
                return a;
            default:
                var p = Pow(a, n / 2);
                return p * p * Pow(a, n % 2);
        }
    }
    public static Modular operator /(Modular a, Modular b)
    {
        return a * Pow(b, M - 2);
    }
    private static readonly List<int> facs = new List<int> { 1 };
    private static Modular Fac(int n)
    {
        for (int i = facs.Count; i <= n; ++i)
        {
            facs.Add((int)(Math.BigMul(facs.Last(), i) % M));
        }
        return facs[n];
    }
    public static Modular Ncr(int n, int r)
    {
        return (n < r) ? 0
             : (n == r) ? 1
                        : Fac(n) / (Fac(r) * Fac(n - r));
    }
    public static explicit operator int(Modular a)
    {
        return (int)a.value;
    }

    public static Modular Lcm(Modular a, Modular b)
    {
        var tmp = Gcdl(a.value, b.value);
        return ((a * b) / new Modular(tmp));
    }
    static Modular Gcd(Modular m, Modular n)
    {
        if (n.value > m.value) return Gcd(n, m);
        if (n.value == 0) return m;
        var r = new Modular(m.value % n.value);
        return Gcd(n, r);
    }

    static long Gcdl(long m, long n)
    {
        if (n > m) return Gcdl(n, m);
        if (n == 0) return m;
        return Gcdl(n, m % n);
    }
}