11029 - Leading and Trailing

11029 - Leading and Trailing

 Topic: Binary Exponentiation

 

	///Binary Exponentiation
	#include <bits/stdc++.h>
	using namespace std;
	#define INF 1<<30
	#define MAX 10005
	#define FASTIO ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	typedef long long ll;
	// compute x^n mod m
	ll binpow(ll a, ll b, ll m = 1000)
	{
	a %= m;
	ll res = 1;
	while(b > 0)
	{
	if(b & 1)
	res = (res * a) % m;
	a = (a * a) % m;
	b >>= 1;
	}
	return res;
	}
	void printLastdigit(ll a, ll b, ll k)
	{
	ll tmp = binpow(a, b, k);
	printf("%03lld", tmp);
	//cout << "..."<< tmp<<endl;
	}
	int main()
	{
	//FASTIO
	///*
	//double start_time = clock();
	#ifndef ONLINE_JUDGE
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w", stdout);
	freopen("error.txt", "w", stderr);
	#endif
	//*/
	int t;
	cin >> t;
	while(t--)
	{
	ll x, y, m;
	cin >> x >> y;
	m = 1000;
	double a = y * log10(x);
	double b = floor(pow(10, a - floor(a) + 3 - 1) ) ;
	cout << b << "...";
	printLastdigit(x, y, m);
	cout << endl;
	}
	//double end_time = clock();
	//printf( "Time = %lf ms\n", ( (end_time - start_time) / CLOCKS_PER_SEC)*1000);
	return 0;
	}

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