Problem:
Score : 600 points

Problem Statement

Find the number of sequences of length K consisting of positive integers such that the product of any two adjacent elements is at most N, modulo 10^9+7.

Constraints

1\leq N\leq 10^9

1 2\leq K\leq 100 (fixed at 21:33 JST)

N and K are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the number of sequences, modulo 10^9+7.

Sample Input 1

3 2

Sample Output 1

5

(1,1), (1,2), (1,3), (2,1), and (3,1) satisfy the condition.

Sample Input 2

10 3

Sample Output 2

147

Sample Input 3

314159265 35

Sample Output 3

457397712

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Security.Cryptography.X509Certificates;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var nk = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
			long n = nk[0];
			int k = (int)nk[1];

			var dic = new Dictionary<long, long>();
			long lastVal = 0;
			for (long i = 1; (i - 1) * (i - 1) < n; i++) {
				long val = n / i;
				if (dic.ContainsKey(val) == false) {
					dic[val] = 1;
				} 

				if (i != 1) {
					dic[i - 1] = lastVal - val;
				}

				lastVal = val;
			}

			int m = dic.Count();
			var keys = dic.Keys.OrderBy(x => x).ToArray();

			var mul = new ModInt[m];
			var dp = new ModInt[k, m];
			for (int i = 0; i < m; i++) {
				mul[i] = dic[keys[m - 1 -i]];
				dp[0, i] = dic[keys[m - 1 - i]]; ;
			}

			for (int i = 1; i < k; i++) {
				for (int j = 0; j < m; j++) {
					for (int l = 0; l < m; l++) {
						if (keys[j] * keys[l] > n) {
							continue;
						}

						dp[i, l] += dp[i - 1, j] * mul[l];
					}
				}
			}

			ModInt ans = 0;
			for (int i = 0; i < m; i++) {
				ans += dp[k - 1, i];
			}

			Console.WriteLine(ans);
		}
	}

	public struct ModInt
	{
		public static long Mod { get; set; } = (long)1e9 + 7;

		public static ModInt Pow(ModInt value, long k)
		{
			return Pow(value.Value, k);
		}

		public static ModInt Pow(long value, long k)
		{
			long ret = 1;
			for (k %= Mod - 1; k > 0; k >>= 1, value = value * value % Mod) {
				if ((k & 1) == 1) {
					ret = ret * value % Mod;
				}
			}
			return new ModInt(ret);
		}

		public static ModInt Inverse(ModInt value)
		{
			return Pow(value, Mod - 2);
		}

		public long Value;

		public ModInt(long value)
		{
			Value = value;
		}

		public static ModInt operator +(ModInt lhs, ModInt rhs)
		{
			lhs.Value += rhs.Value;
			if (lhs.Value >= Mod) {
				lhs.Value -= Mod;
			}
			return lhs;
		}

		public static ModInt operator -(ModInt lhs, ModInt rhs)
		{
			lhs.Value -= rhs.Value;
			if (lhs.Value < 0) {
				lhs.Value += Mod;
			}

			return lhs;
		}

		public static ModInt operator *(ModInt lhs, ModInt rhs)
		{
			return new ModInt(lhs.Value * rhs.Value % Mod);
		}
		public static ModInt operator /(ModInt lhs, ModInt rhs)
		{
			long exp = Mod - 2;
			while (exp > 0) {
				if (exp % 2 > 0) {
					lhs *= rhs;
				}

				rhs *= rhs;
				exp /= 2;
			}

			return lhs;
		}

		public static implicit operator ModInt(long n)
		{
			n %= Mod;
			if (n < 0) {
				n += Mod;
			}

			return new ModInt(n);
		}

		public override string ToString()
		{
			return Value.ToString();
		}
	}
}