P4620 [SDOI2018] Honorary Title

- Input file: title.in - Output file: title.out - Time limit: 10 seconds. - Memory limit: 512 megabytes.

Casual game player $Q$ has not only achieved excellent results in algorithm contests, but also ranks very high in a diamond-collecting game. This game has $n$ different types of diamonds, numbered from $1$ to $n$. Player $Q$ has played this game for a long time. For type $i$, he has already collected $a_i$ diamonds. The biggest feature of this game is that there is only one way to obtain diamonds: buying them from the shop. Specifically, the unit price of type $i$ is $b_i$ coupons. To encourage players to spend money, there is no quantity limit for any type of diamond: as long as you are willing to pay, you can have as many diamonds as you want. However, the game does not have a “discard item” feature, so $Q$ cannot discard diamonds to complete the task. Recently, the game launched a limited-time achievement task. Players who complete it can get an honorary title. The completion condition is: Given positive integers $k$ and $m$, for any integer $x \ (x\ge 2^k)$, the value $a_{x}+a_{\lfloor\frac{x}{2}\rfloor}+a_{\lfloor\frac{x}{4}\rfloor}+a_{\lfloor\frac{x}{8}\rfloor}+...+a_{\lfloor\frac{x}{2^k}\rfloor}$ must be a multiple of $m$. Of course, skilled player $Q$ wants to complete this limited-time achievement task, but before spending money he wants to know how many coupons he needs to complete it. Please write a program to help $Q$ compute the minimum number of coupons required.

The first line contains a positive integer $T$, the number of test cases. For each test case, the first line contains $9$ positive integers $n, k, m, p, SA, SB, SC, A, B$, where $n$ is the number of diamond types, and $k, m$ are the task conditions. To reduce the input size to some extent, arrays $a[]$ and $b[]$ are generated by the following code: ``` unsigned int SA, SB, SC;int p, A, B; unsigned int rng61(){ SA ^= SA > 5; SA ^= SA

For each test case, output one integer per line, the minimum number of coupons required.

- $1 ≤ T ≤ 10$. - $1 ≤ k ≤ 10$ and $2^k ≤ n$. - $1 ≤ p ≤ min(n, 100000)$, $10000 ≤ SA, SB, SC ≤ 1000000$. - $1 ≤ A, B, ai, bi ≤ 10^7$. Constraints: Subtask 1 ($30$ points): $1 ≤ n ≤ 1000$ and $m = 2$. Subtask 2 ($40$ points): $1 ≤ n ≤ 10^5$ and $m ≤ 200$. Subtask 3 ($30$ points): $1 ≤ n ≤ 10^7$ and $m ≤ 200$. Translated by ChatGPT 5