Matrix Quick Power Template

Description

In the Fibonacci integer sequence, f_0 = 0, f_1 = 1, and f_n = f_{n-1} + f_{n-2} for n \geq 2. For example, the first ten terms of the Fibonacci sequence is:

0, 1, 1, 2, 3, 5, 8, \cdots

An alternative formula for the Fibonacci sequence is

Given an integer n, your goal was to compute the last 4 digits of f_n.

Input

The input test file would contain multiple test cases. Each test case consists of a containing n (where 0 \leq n \leq 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 f_n. If the last four digits of f_n is all zeros, print 0 ; otherwise, omit any leading zeros (i.e., print f_n< c6> mod 10000).

Sample Input

0
9
999999999
1000000000
-1

Sample Output

0
34
626
6875

Hint

As a reminder, matrix multiplication is associative, and the product of the 2 \times 2 matrices are givenby

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

The data used in this problem are unofficial data prepared by 695375900. So any mistake this does not imply mistake in the offcial judge data.

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <algorithm>5#include <cmath>6#include <sstream>7#include <string>8 using namespacestd;9 #defineM 10000Ten structMatrix One { A     inta[2][2]; - }; - Matrix Mul (Matrix X,matrix y) the { - Matrix temp; -memset (TEMP.A,0,sizeof(TEMP.A)); -      for(intI=0;i<2; i++) +          for(intj=0;j<2; j + +) -          for(intk=0;k<2; k++) +Temp.a[i][j]= (Temp.a[i][j]+x.a[i][k]*y.a[k][j])%M; A     returntemp; at } -Matrix Mpow (Matrix A,intN) - { - matrix B; -memset (B.A,0,sizeof(B.A)); -      for(intI=0;i<2; i++) inb.a[i][i]=1; -      while(n>0) to     { +         if(n&1) -b=Mul (b,a); theA=Mul (a,a); *n>>=1; $     }Panax Notoginseng     returnB; - } the intMain () + { A matrix A; the    intN; +     while(~SCANF ("%d",&N)) -    { $a.a[0][0]=1; a.a[0][1]=1; $a.a[1][0]=1; a.a[1][1]=0; -     if(n==-1) -     Break; the     if(n==0) -{printf ("0\n");Wuyi    Continue;} the    if(n==1) -{printf ("1\n"); Wu     Continue;} -  AboutA=Mpow (a,n); $printf"%d\n", a.a[1][0]);} -     return 0; -}

Matrix Quick Power Template