E. Decimal Expansion

Codeforces

IDCF10235E

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Consider the following constant: $$\varphi = \dfrac{9}{10} \cdot \dfrac{99}{100} \cdot \dfrac{999}{1000} \cdot \dfrac{9999}{10000}\cdot \dots$$ You have to find the $n$-th digit after the decimal separator in the decimal representation of $phi.alt$. The first line of input contains a single integer $t$ ($1 <= t <= 10^5$) which is the number of test cases. The next line contains $t$ integers $n$ ($1 <= n <= 10^(18)$), one for each test case. For each test case, output a single digit which is the answer to that test case. Separate consecutive answers by single spaces. The constant evaluates as $phi.alt = 0. 890010099998999 \\dots$ ## Input The first line of input contains a single integer $t$ ($1 <= t <= 10^5$) which is the number of test cases.The next line contains $t$ integers $n$ ($1 <= n <= 10^(18)$), one for each test case. ## Output For each test case, output a single digit which is the answer to that test case. Separate consecutive answers by single spaces. [samples] ## Note The constant evaluates as $phi.alt = 0. 890010099998999 \\dots$

**Definitions** Let $\varphi = \prod_{k=1}^{\infty} \left(1 - 10^{-k}\right)$. **Constraints** 1. $1 \le t \le 10^5$ 2. For each test case, $1 \le n \le 10^{18}$ **Objective** For each test case, find the $n$-th digit after the decimal point in the decimal expansion of $\varphi$.

API Response (JSON)

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