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No.1407 Kindness

レベル : / AI推定難易度 : 1700 / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 158
作問者 : PCTprobability / テスター : akakimidori Izayoi_R_sakura
お気に入りにしたユーザー ProblemId : 5593 / 自分の提出
問題文最終更新日: 2021-02-26 23:28:43
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Problem Statement

You are given a positive integer $N$. PCT-kun wanted to know the sum, over all positive integers from $1$ to $N$, of the product of the digits of each integer, but he could not compute it. So, in his place, please find the sum, over all positive integers from $1$ to $N$, of the product of the digits of each integer. Since the answer can be very large, output the remainder when it is divided by $1000000007$.

Input

$N$

  • All inputs are integers.
  • $1 \le N \le 10^{100000}$

Output

Find the sum, over all positive integers from $1$ to $N$, of the product of the digits of each integer. Since the answer can be very large, output the remainder when it is divided by $1000000007$.

Sample

Sample 1
Input
12
Output
48

Since $1+2+3+4+5+6+7+8+9+1×0+1×1+1×2=48$, output $48$.

Sample 2
Input
1234567890987654321
Output
333144460

The input can be very large. Also, note that you must find the remainder when the answer is divided by $1000000007$.

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