Asset Depreciation by Three Methods

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

An asset has an initial value $V$ and an expected life of $n$ years. Depreciation is deducted from its remaining value, initially $V$. Choose one method using code $m$:

• $m=1$ — Straight line: deduct the constant amount $V/n$ each year.
• $m=2$ — Declining balance: deduct $2/n$ times the remaining value at the beginning of the current year.
• $m=3$ — Sum of years: let $S=1+2+\cdots+n$. During year $i$ (numbered starting from $1$), deduct $V(n-i+1)/S$ based on the original value.

Print the remaining value after each year in order. Keep unrounded intermediate values and round only each printed value. For methods 1 and 3, the remaining value after the final year is defined as zero to eliminate tiny floating-point artifacts.

Input

One line contains the real value $V$ and the integers $n$ and $m$, in that order. $V$ is the initial asset value, $n$ is the number of years and $m$ chooses the method.

Output

Print exactly $n$ lines. Line $i$ contains the integer $i$, one space, and the remaining value immediately after year $i$, formatted with exactly two decimal digits. Do not print column headings or a currency symbol.

Subtasks

• Subtask 1 (20%): $0<V\le10^6,\ 2\le n\le100,\ m=1$.
• Subtask 2 (30%): $0<V\le10^6,\ 2\le n\le100,\ m\in\{1,2\}$.
• Subtask 3 (50%): $0<V\le10^6,\ 2\le n\le100,\ m\in\{1,2,3\}$.

Examples

Example 1

Input:

100 4 1

Output:

1 75.00
2 50.00
3 25.00
4 0.00

Explanation: The fixed annual deduction is 100/4 = 25. The remaining values are 75, 50, 25 and 0.

Example 2

Input:

100 4 2

Output:

1 50.00
2 25.00
3 12.50
4 6.25

Explanation: The annual rate is 2/4 = 0.5. Successive remaining values are 50, 25, 12.5 and 6.25.

Example 3

Input:

100 4 3

Output:

1 60.00
2 30.00
3 10.00
4 0.00

Explanation: The year weights sum to 10. Deducting 40, 30, 20 and 10 from the initial 100 gives remaining values 60, 30, 10 and 0.