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;
using static Scanner;

class Program
{
    public static void Main()
    {
        int n = ReadInt();
        int k = ReadInt();
        var s = new List<int>();
        for (int i = 0; i < k; i++)
        {
            int l = ReadInt();
            int r = ReadInt();
            s.AddRange(Enumerable.Range(l, r - l + 1));
        }
        ModInt[] dp = new ModInt[n];
        dp[0] = 1;
        for (int i = 0; i < n; i++)
        {
            foreach (int j in s)
            {
                if (i - j < 0) continue;
                dp[i] += dp[i - j];
            }
        }
        Console.WriteLine((int)dp[n - 1]);
    }
}

static class Scanner
{
    static Queue<string> que = new Queue<string>();
    public static string Read() { if (!que.Any()) foreach (var s in Console.ReadLine().Split()) que.Enqueue(s); return que.Dequeue(); }
    public static int ReadInt() => int.Parse(Read());
    public static long ReadLong() => long.Parse(Read());
    public static IEnumerable<string> Read(long n) { for (long i = 0; i < n; i++) yield return Read(); }
    public static IEnumerable<int> ReadInt(long n) => Read(n).Select(int.Parse);
    public static IEnumerable<long> ReadLong(long n) => Read(n).Select(long.Parse);
}

struct ModInt
{
    const int MOD = 998244353;// 1000000007;
    long value;
    static List<ModInt> fact = new List<ModInt> { 1 };
    public ModInt(long value) => this.value = value;
    public static implicit operator ModInt(long a) => new ModInt(a % MOD + (a < 0 ? MOD : 0));
    public static explicit operator int(ModInt a) => (int)a.value;
    public static ModInt operator +(ModInt a, ModInt b) => a.value + b.value;
    public static ModInt operator -(ModInt a, ModInt b) => a.value - b.value;
    public static ModInt operator *(ModInt a, ModInt b) => a.value * b.value;
    public static ModInt operator /(ModInt a, ModInt b) => a * Inv(b);
    public static ModInt Pow(ModInt a, int n) { if (n == 0) return 1; if (n == 1) return a; var p = Pow(a, n / 2); return p * p * Pow(a, n % 2); }
    public static ModInt Inv(ModInt a) => Pow(a, MOD - 2);
    public static ModInt Fact(int n) { for (int i = fact.Count; i <= n; i++) fact.Add(fact[^1] * i); return fact[n]; }
    public static ModInt Npr(int n, int r) => Fact(n) / Fact(n - r);
    public static ModInt Ncr(int n, int r) => Fact(n) / Fact(n - r) / Fact(r);
    public static ModInt Nhr(int n, int r) => Fact(n + r - 1) / Fact(n - 1) / Fact(r);
}