快速幂等差数列
\(a_i+a_{i+2}=a_{i+1}*2\)为等差数列，根据通项\(a_n=a_1+(n-1)*d\)就可以求出第n项。
而对于等比数列，\(a_n=a_1*q^{n-1}\)，q的n-1次幂。
#include<cstdio>
#include<cstring>
#define ll long long
using namespace std;
const ll M = 200907;
ll pow(ll x, ll y)//快速幂
{
ll ans_ = 1;
while(y)
{
if(y%2==1) ans_*=x;
x = (x*x)%M;
y = y/2;
}
return ans_;
}
ll a, b, c, d, k, ans;
void s()
{
scanf("%lld%lld%lld%lld", &a, &b, &c, &k);
if(c-b == b-a)
{
d = (b-a)%M;
ans = (a+(k-1)%M*d)%M;
}//判断是否为等差数列
else
{
d = (b/a)%M;
ans = a%M*pow(d, k-1)%M;
}//否则为等比数列
printf("%lld\n", ans);
}
int t;
int main()
{
scanf("%d", &t);
while(t--) s();
return 0;
}