# MAIN74 spoj Solution - Correct, Optimal and Working

``````/*
* MAIN74.cpp
*
*  Created on: Jun 22, 2014
*      Author: Arpit Bhayani
*/

#include <stack>
#include <cstdio>
#include <cstdlib>
#include <iostream>

using namespace std;

#define DEBUG 0
#define gc getchar
#define ll long long

void scanint(ll int &x) {
register ll int c = gc();
x = 0;
for (; (c < 48 || c > 57); c = gc())
;
for (; c > 47 && c < 58; c = gc()) {
x = (x << 1) + (x << 3) + c - 48;
}
}

int i = 0;
char ch;
while ((ch = getchar()) != '\n') {
str[i++] = ch;
}
str[i] = '\0';
return i;
}

#define MOD 1000000007

ll int fib(ll int n) {

n--;
stack<int> s;

ll int m[2][2] = { { 1LL, 1LL }, { 1LL, 0LL } };
ll int f[2][2] = { { 1LL, 1LL }, { 1LL, 0LL } };

while (n) {
s.push(n & 1);
n /= 2;
}

s.pop();

ll int w, x, y, z;
while (!s.empty()) {

w = ((f[0][0] * f[0][0]) % MOD + (f[0][1] * f[1][0]) % MOD) % MOD;
x = ((f[0][0] * f[0][1]) % MOD + (f[0][1] * f[1][1]) % MOD) % MOD;
y = ((f[1][0] * f[0][0]) % MOD + (f[1][1] * f[1][0]) % MOD) % MOD;
z = ((f[1][0] * f[0][1]) % MOD + (f[1][1] * f[1][1]) % MOD) % MOD;
f[0][0] = w;
f[0][1] = x;
f[1][0] = y;
f[1][1] = z;

if (s.top() == 1) {

w = ((f[0][0] * m[0][0]) % MOD + (f[0][1] * m[1][0]) % MOD) % MOD;
x = ((f[0][0] * m[0][1]) % MOD + (f[0][1] * m[1][1]) % MOD) % MOD;
y = ((f[1][0] * m[0][0]) % MOD + (f[1][1] * m[1][0]) % MOD) % MOD;
z = ((f[1][0] * m[0][1]) % MOD + (f[1][1] * m[1][1]) % MOD) % MOD;
f[0][0] = w;
f[0][1] = x;
f[1][0] = y;
f[1][1] = z;
}

s.pop();
}

return f[0][0];
}

int main(int argc, char * argv[]) {

int t;
scanf("%d", &t);
while (t--) {
ll int x;
scanf("%lld", &x);

if (x == 0)
printf("0\n");
else if (x == 1)
printf("2\n");
else
printf("%lld\n", fib(x + 3) % MOD);
}
return 0;
}
``````