Problem Description

Xiao Lan is doing a security evaluation for an encryption algorithm based on big integer multiplication. During the evaluation, he uses this algorithm to generate two special keys $A$ and $B$:

• Key $A$ consists of $20260606$ digits $9$, that is, $A = \underbrace{99...9}_{20260606\text{ digits}}$.
• Key $B$ consists of $2026$ digits $9$, that is, $B = \underbrace{99...9}_{2026\text{ digits}}$.

By computing their product, Xiao Lan gets an extremely long combined key $S = A \times B$.

To verify the integrity of this key during transmission, Xiao Lan needs to extract the digits at specific positions in the decimal representation of $S$ (counting from left to right, with no leading zeros). Let $d_1, d_2, d_3$ be the digits at the $2026$-th, $20260523$-rd, and $20262632$-nd positions of $S$, respectively.

Now, please find the value of the three-digit integer $\overline{d_1 d_2 d_3}$ formed by these three extracted digits in order. Here $d_1$ is the hundreds digit (it is guaranteed that $d_1 \ne 0$), $d_2$ is the tens digit, and $d_3$ is the ones digit. For example, if the three extracted digits are $d_1 = 2, d_2 = 5, d_3 = 7$, then the answer you should submit is $257$.

Output Format

This is an output-only (fill-in-the-blank) problem. You only need to compute the result and submit it. The result of this problem is an integer. When submitting, you only need to write a program that outputs this integer. Any extra content will result in no score.

Hint

Translated by ChatGPT 5