D. Treasure Box

Codeforces

IDCF10054D

Time2000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Your team was exploring an ancient city. Suddenly you found an old scroll with 2 integer numbers N and K, which encrypts the secret code to open a treasure box. Considering a transformation on an integer X described as follows: X = X + X mod 100, the secret code can be obtained by applying the above-described transformation K times successively to N. The input file consists of several datasets. The first line of the input file contains the number of datasets which is a positive integer and is not greater than 500. Each dataset has two space-separated positive integers N and K (1 ≤ N ≤ 109, 1 ≤ K ≤ 109) written on a single line. For each dataset, write on a single line the secret number decrypted from N and K. ## Input The input file consists of several datasets. The first line of the input file contains the number of datasets which is a positive integer and is not greater than 500. Each dataset has two space-separated positive integers N and K (1 ≤ N ≤ 109, 1 ≤ K ≤ 109) written on a single line. ## Output For each dataset, write on a single line the secret number decrypted from N and K. [samples]

**Definitions** Let $ t \in \mathbb{Z} $ be the number of datasets. Let $ D = \{(N_j, K_j) \mid j \in \{1, \dots, t\}\} $ be the set of datasets, where for each $ j $: - $ N_j \in \mathbb{Z}^+ $ is the initial integer. - $ K_j \in \mathbb{Z}^+ $ is the number of transformations. **Constraints** 1. $ 1 \le t \le 500 $ 2. For each $ j \in \{1, \dots, t\} $: - $ 1 \le N_j \le 10^9 $ - $ 1 \le K_j \le 10^9 $ **Objective** For each dataset $ j $, define the transformation $ f(x) = x + (x \bmod 100) $. Compute the result after $ K_j $ applications: $$ R_j = f^{K_j}(N_j) $$ where $ f^k $ denotes the $ k $-fold composition of $ f $.

API Response (JSON)

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Full JSON Raw Segments