# Hdoj 2817 A sequence of numbers (fast power modulo)

Source: Internet
Author: User

A sequence of numbers http://acm.hdu.edu.cn/showproblem.php?pid=2817
Time limit:2000/1000 MS (java/others) Memory limit:32768/32768 K (java/others)
Total submission (s): 4046 Accepted Submission (s): 1242

problem DescriptionXINLV wrote some sequences on the paper a long time ago, they might is arithmetic or geometric sequences. The numbers is not very clear now, and only the first three numbers of each sequence is recognizable. XINLV wants to know some numbers in these sequences, and he needs your help.
InputThe first line contains a integer n, indicting that there is n sequences. Each of the following N lines contain four integers. The first three indicating the first three numbers of the sequence, and the last one are K, indicating that we want to know The k-th numbers of the sequence.

You can assume 0 < K <= 10^9, and the other three numbers is in the range [0, 2^63]. All the numbers of the sequences is integers. And the sequences are non-decreasing.

OutputOutput one line for each test case, which is, the k-th number module (%) 200907.
Sample Input
`21 2 3 51 2 4 5`

Sample Output
`516`

Sourcemulti-university Training Contest 1-host by Tju
recommendGaojie | We have carefully selected several similar problems for you:2818 2819 2825 2824 2822

#include <cstdio>

#include <cmath>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace Std;
const int mod=200907;
__int64 fun1 (__int64 q,__int64 N)//a1*q^ (n-1)//geometric series
{
__int64 ans=1,base=q;
while (n)
{
if (n&1)
Ans=ans*base%mod;
Base=base*base%mod;
n>>=1;
}
return ans%mod;
}

__int64 fun2 (__int64 a1,__int64 d,__int64 N)//a1+ (n-1) *d;
{
Return a1%mod+ ((n-1)%mod*d%mod)%mod;
}

int Jude (__int64 num1,__int64 Num2,__int64 num3)
{
if (num1+num3==2*num2)
return 0;
Else
return 1;
}

int main ()
{
int n;
scanf ("%d", &n);
while (n--)
{
__int64 a1,a2,a3,k;
scanf ("%i64d%i64d%i64d%i64d", &a1,&a2,&a3,&k);
if (Jude (A1,A2,A3))
{
__int64 q=a3/a2;
printf ("%i64d\n", (A1%MOD*FUN1 (q,k-1)%mod)%mod);
}
Else
{
__int64 d=a3-a2;
printf ("%i64d\n", Fun2 (a1,d,k)%mod);
}
}
return 0;
}

Hdoj 2817 A sequence of numbers (fast power modulo)

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