Contest Duration: - (local time) (100 minutes) Back to Home
G - Edge Elimination /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

T 個のテストケースについて、以下の問題を解いてください。

あなたの目標はこの木の辺を何本か切って、連結成分のうちいずれかを X 頂点にすることです。

### 制約

• 入力は全て整数
• 1 \le T \le 100
• 1 \le D
• 2 \le K
• \displaystyle 1 \le X \le \sum_{i=0}^{D} K^i \le 10^{18}

T
case_1
\vdots
case_T

D K X

### 出力

そのうち i 行目には i 個目のテストケースに対する答えを整数として出力せよ。

### 入力例 1

11
2 2 1
2 2 2
2 2 3
2 2 4
2 2 5
2 2 6
2 2 7
1 999999999999999999 1
1 999999999999999999 2
1 999999999999999999 999999999999999999
1 999999999999999999 1000000000000000000

### 出力例 1

1
2
1
1
2
1
0
1
999999999999999998
1
0

Score : 600 points

### Problem Statement

Solve the following problem for T test cases.

We have a perfect K-ary tree of depth D (with 1+K+K^2+\dots+K^D vertices).
Your objective is to cut some of the edges to obtain a connected component with exactly X vertices.
At least how many edges must be cut to achieve the objective?

### Constraints

• All values in the input are integers.
• 1 \le T \le 100
• 1 \le D
• 2 \le K
• \displaystyle 1 \le X \le \sum_{i=0}^{D} K^i \le 10^{18}

### Input

The input is given from Standard Input in the following format:

T
case_1
\vdots
case_T

Here, case_i denotes the i-th test case.
Each test case is given in the following format:

D K X

### Output

Print T lines.
The i-th line should contain the answer to the i-th test case as an integer.

### Sample Input 1

11
2 2 1
2 2 2
2 2 3
2 2 4
2 2 5
2 2 6
2 2 7
1 999999999999999999 1
1 999999999999999999 2
1 999999999999999999 999999999999999999
1 999999999999999999 1000000000000000000

### Sample Output 1

1
2
1
1
2
1
0
1
999999999999999998
1
0