Problem:
Score : 900 points

Problem Statement

For a positive integer n, let us define f(n) as the number of digits in base 10.

You are given an integer S.
Count the number of the pairs of positive integers (l, r) (l \leq r) such that f(l) + f(l + 1) + ... + f(r) = S, and find the count modulo 10^9 + 7.

Constraints

1 \leq S \leq 10^8

Input

Input is given from Standard Input in the following format:

S

Output

Print the answer.

Sample Input 1

1

Sample Output 1

9

There are nine pairs (l, r) that satisfies the condition: (1, 1), (2, 2), ..., (9, 9).

Sample Input 2

2

Sample Output 2

98

There are 98 pairs (l, r) that satisfies the condition, such as (1, 2) and (33, 33).

Sample Input 3

123

Sample Output 3

460191684

Sample Input 4

36018

Sample Output 4

966522825

Sample Input 5

1000

Sample Output 5

184984484

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

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


class Solver {
  const int M = 9999999;
  const int MOD = 1000000007;
  public long exp(long x, long t) {
    if (t == 0) return 1;
    long ret = exp(x, t >> 1);
    ret = ret * ret % MOD;
    if ((t & 1) == 1) ret = ret * x % MOD;
    return ret;
  }
  public int f(int x) {
    if (x <= 9) return 1;
    if (x <= 99) return 2;
    if (x <= 999) return 3;
    if (x <= 9999) return 4;
    if (x <= 99999) return 5;
    if (x <= 999999) return 6;
    if (x <= 9999999) return 7;
    return 8;
  }
  public void solve() {
    int n = cin.readInt();
    long ans = 0;
    for (int i = 1, r = 1, sum = 0; i <= M; i++) {
      while (sum < n && r <= M) {
        sum += f(r); r++;
      }
      if (sum < n) {
        if ((n - sum) % 8 == 0) ans++;
      } else {
        if (sum == n) ans++;
      }
      sum -= f(i);
    }
    List<int> fac = new List<int>();
    for (int i = 1; i * i <= n; i++) {
      if (n % i != 0) continue;
      fac.Add(i);
      if (n/i != i) fac.Add(n/i);
    }
    foreach(int x in fac) {
      if (x < 8) continue;
      ans += (exp(10, x-1) * 9) - (n / x - 1) + MOD;
      ans %= MOD;
    }
    {
      int r = n / 8;
      ans += r;
      ans %= MOD;
      foreach (int x in fac) {
        if (x < 8) continue;
        if (n/x <= r) {
          ans += MOD - 1;
          ans %= MOD;
        }
      }
    }
    ans = (ans % MOD + MOD) % MOD;
    Console.Out.WriteLine(ans);
  }

  public Istream cin = new Istream(Console.OpenStandardInput());
  static public void swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
}


#region Istream
class Istream {
  public Istream(Stream _ins) { ins = _ins; }

  const int BUF_SZ = 1024;
  private Stream ins;
  private byte[] buf = new byte[BUF_SZ];
  private int len, ptr;

  private byte readByte() {
    if (ptr >= len) {
      ptr = 0;
      len = ins.Read(buf, 0, BUF_SZ);
      if (len == 0) return 0;
    }
    return buf[ptr++];
  }
  public char nextChar() {
    byte b;
    do b = readByte(); while (b < 33 && 126 < b);
    return (char)b;
  }
  public string read() {
    var sb = new StringBuilder();
    for (char c = nextChar(); (33 <= c && c <= 126); c = (char)readByte()) sb.Append(c);
    return sb.ToString();
  }
  public string readLine() {
    var sb = new StringBuilder();
    for (char c = nextChar(); (c != '\n' && c != 0); c = (char)readByte()) sb.Append(c);
    return sb.ToString();
  }
  public long readLong() { return long.Parse(read()); }
  public int readInt() { return int.Parse(read()); }
  public double readDouble() { return double.Parse(read()); }
}
#endregion


#region Main
class ReSha {
  static void Main() {
    new Solver().solve();
  }
}
#endregion