Fibonacci

In the Fibonacci integer sequence, F₀ = 0, F₁ = 1, and F_n = F_{n − 1} + F_{n − 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 F_n.

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 F_n. If the last four digits of F_nare all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print F_n mod 10000).

Sample Input

099999999991000000000-1

Sample Output

0346266875

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:

.

#include<stdio.h>#include<string.h>typedef struct Matrix{int M[5][5];Matrix(){memset(M,0,sizeof(M));}}Matrix;Matrix M_multi(Matrix m1,Matrix m2,int n){Matrix m3;for(int i=0;i<n;i++){for(int j=0;j<n;j++){for(int k=0;k<n;k++){m3.M[i][j]+=(m1.M[i][k]%10000)*(m2.M[k][j]%10000);}m3.M[i][j]%=10000;}}return m3;}int main(){int k;while(scanf("%d",&k),k!=-1){Matrix t,s;s.M[0][0]=1,s.M[1][1]=1;t.M[0][0]=1,t.M[0][1]=1,t.M[1][0]=1,t.M[1][1]=0;while(k){if(k&1)s=M_multi(s,t,2);t=M_multi(t,t,2);k>>=1;}printf("%d\n",s.M[1][0]%10000);}return 0;}