poj3070--Fibonacci(矩阵的高速幂)

Fibonacci

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 9650		Accepted: 6856

Description

In the Fibonacci integer sequence, F0 = 0, F1 = 1, and Fn = Fn −
1 + Fn − 2 for n ≥ 2. For example, the first ten terms of the Fibonacci sequence are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

An alternative formula for the Fibonacci sequence is


.

Given an integer n, your goal is to compute the last 4 digits of Fn.

Input

The input test file will contain multiple test cases. Each test case consists of a single line containing n (where 0 ≤ n ≤ 1,000,000,000). The end-of-file is denoted by a single line containing the number −1.

Output

For each test case, print the last four digits of Fn. If the last four digits of Fn are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print Fn mod
10000).

Sample Input

0
34
626
6875

Hint

As a reminder, matrix multiplication is associative, and the product of two 2 × 2 matrices is given by


.

Also, note that raising any 2 × 2 matrix to the 0th power gives the identity matrix:


.

Source

Stanford Local 2006
和普通的高速幂的写法同样，不同的是须要计算矩阵相乘，仅仅要写对矩阵的乘法，就没难度了