Jzzhu and sequences (matrix fast power + modulo)

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Jzzhu have invented a kind of sequences, they meet the following property:

　　　　　　　　　　　　

You is given x and y, please calculate f_{n modulo 1000000007 (Ten^9?+?7).}

Input

The first line contains integers x and y (| X|,?| y|? ≤?10^{9). The second line contains a single integer n (1?≤? N? ≤?2 109).}

Output

Output a single integer representing f_{n modulo 1000000007 (Ten^9?+?7).}

ExamplesInput

2 3
3

Output

1

Input

0-1
2

Output

1000000006

Note

In the first sample, f_{2?=? F1?+? F3, 3?=?2?+? F3, f3?=?1.}

In the second sample, f_{2?=?? -?1; ?-? 1 modulo (ten^{9?+?7) equals (9?+?6).}}

AC Code:

1#include <iostream>2#include <cstring>3#include <cstdio>4 using namespacestd;5 structmatrix{6     Long Long intmat[3][3];7 }a,b;8 Long Long intMoDLong Long intN) {9     if(N >0)Ten         returnN%1000000007; One     Else if(N <0) A         return(n +1000000007) %1000000007; -     Else -         return 0; the } - Matrix Mul (Matrix A,matrix b) { - matrix tmp; -memset (Tmp.mat,0,sizeof(Tmp.mat)); +      for(inti =0; I <3; i++) -          for(intj =0; J <3; j + +) +              for(intK =0; k <3; k++){ ATMP.MAT[I][J] + = a.mat[i][k] *B.mat[k][j]; atTMP.MAT[I][J] =mod (tmp.mat[i][j]); -             } -     returntmp; - } -Matrix Pow_mat (Matrix A,intN) { - matrix ans; inmemset (Ans.mat,0,sizeof(Ans.mat)); -      for(inti =0; I <3; i++) toAns.mat[i][i] =1; +      while(n) { -         if(N &1) theAns =Mul (ans,a); *A =Mul (a,a); $N >>=1;Panax Notoginseng     } -     returnans; the } + intMain () { A     Long Long intX,y,n; thescanf"%lld%lld%lld",&x,&y,&n); +     if(n = =1) -printf"%lld\n", mod (x)); $     Else if(n = =2) $printf"%lld\n", mod (y)); -     Else if(n = =3) -printf"%lld\n", MoD (Y-x +1000000007));//Notice the modulus here the     Else{ -a.mat[0][0] = x,a.mat[0][1] = y,a.mat[0][2] = y-x;Wuyib.mat[0][0] =0, b.mat[0][1] =0, b.mat[0][2] =0; theb.mat[1][0] =1, b.mat[1][1] =0, b.mat[1][2] = -1; -b.mat[2][0] =0, b.mat[2][1] =1, b.mat[2][2] =1; WuB = Pow_mat (B,n-3); -printf"%lld\n", MoD (Mul (A, b). mat[0][2])); About     } $     return 0; -}

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Jzzhu and sequences (matrix fast power + modulo)