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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static ABC.Cin;
using static ABC.Cout;
using static ABC.Tool;


namespace ABC
{
    class Program
    {
        static void Main(string[] args)
        {
            Scanf(out int n, out int k);
            var L = new int[k];
            var R = new int[k];
            for(int i = 0; i < k; i++)
            {
                Scanf(out L[i], out R[i]);
            }

            var MOD = 998244353;
            var dp = new long[n + 1];
            dp[0] = 0;
            dp[1] = 1;
            for(int i = 2; i <= n; i++)
            {
                for(int j = 0; j < k; j++)
                {
                    if(i - L[j] > 0)
                    {
                        dp[i] = (dp[i] + dp[i - L[j]]) % MOD;
                    }
                    if(i - R[j] - 1 > 0)
                    {
                        dp[i] = (dp[i] - dp[i - R[j] - 1] + MOD) % MOD;
                    }
                }
                dp[i] += dp[i - 1];
                dp[i] %= MOD;
            }
            OutL(dp[n] - dp[n - 1]);
        }
    }

    static class Cin
    {
        public static string[] ReadSplit => Console.ReadLine().Split();
        public static int[] ReadSplitInt => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] ReadSplitLong => Console.ReadLine().Split().Select(long.Parse).ToArray();
        public static string Str => Console.ReadLine();
        public static int Int => int.Parse(Console.ReadLine());
        public static long Long => long.Parse(Console.ReadLine());
        public static double Double => double.Parse(Console.ReadLine());
        public static T Conv<T>(string input)
        {
            return (T)Convert.ChangeType(input, typeof(T));
        }
        public static void Scanf<T>(out T a) => a = Conv<T>(Console.ReadLine());
        public static void Scanf<T,U>(out T a, out U b)
        {
            var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]);
        }
        public static void Scanf<T, U, V>(out T a, out U b, out V c)
        {
            var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]);
        }
        public static void Scanf<T, U, V, W>(out T a, out U b, out V c, out W d)
        {
            var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]); d = Conv<W>(q[3]);
        }
    }
    static class Cout
    {
        public static void OutL(object s) => Console.WriteLine(s);
    }
    static class Tool
    {
        public static long Gcd(long a, long b)
        {
            if (a % b == 0)
            {
                return b;
            }
            else
            {
                return Gcd(b, a % b);
            }
        }
        public static long Lcm(long a, long b) => a * b / Gcd(a, b);

        public static long[] PrimeFac(long n)
        {
            var result = new long[n + 1];
            for(int i = 2; i * i <= n; i++)
            {
                if (n % i != 0)
                {
                    continue;
                }

                var cnt = 0;
                while(n % i == 0)
                {
                    cnt++;
                    n /= i;
                }
                result[i] = cnt;
            }
            if(n != 1)
            {
                result[n] = 1;
            }
            return result;
        }
        public static long DivsCnt(long n)
        {
            var result = 1L;
            for (int i = 2; i * i <= n; i++)
            {
                if (n % i != 0)
                {
                    continue;
                }

                var cnt = 0;
                while (n % i == 0)
                {
                    cnt++;
                    n /= i;
                }
                result *= (cnt + 1);
            }
            if (n != 1)
            {
                result *= 2;
            }
            return result;
        }
    }
}