Problem E: Fibonacci数列(二)

上一题 正确率: $77.64\%$ 下一题
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Time Limit $1$ 秒/Second(s) Memory Limit $512$ 兆字节/Megabyte(s)
提交总数 $738$ 正确数量 $573$
裁判形式 标准裁判/Standard Judge 我的状态 尚未尝试
难度 分类标签 二分 矩阵快速幂 数论

Description

描述

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复制

0
9
1000000000
-1

Sample Output复制

0
34
6875

提示

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:

.