Age of the Great Voyages

Problem Description
"Age of the Great Voyages", which is also called "Uncharted Waters", is an old PC-game telling an interesting story in the period between the 15-th century and the 17-th century, when European explorers sailed the seas to open new alternative ways to Asia when the Ottoman Empire blocked the land routes.

The story evolves on the search of the seven "Proof of the Conqueror", which are seven ancient artifacts, in seven areas around the world (Northern Europe, Mediterranean, Africa, New World, Indian Ocean, South Asia and East Asia). It is said that having these proofs proves that the sailor is the champion of all sailors. Four sailors unwittingly involved in the struggle of the quest of the search of the Proof of the Conqueror.

  • from wikipedia

Li Huamei, an Admiral of Ming Dynasty, is one of the four protagonists in the story. She trys to find the "Proof of the Conqueror" for the revitalization of the motherland. One person's power is limited, so she searches for like-minded people to help her.

When Li's fleet voyages to the New World, she meets an intelligent man - Fernandes and invite him to become a member of the fleet as a staff officer. While Fernandes is a strange man, he requires that he will join only if Li can win in the following game:

At the beginning, there are N piles of coins on the desk, the i-th pile has Pi coins. Then Fernandes and Li take turns to take coins from those piles on the desk according to the following rule: when it is someone's turn to take coins, at first, he/she has to select no more than K (and no less than 1) piles that still have coins arbitrarily, then take arbitrary number (at least 1) of coins from each piles he/she selects. The game is over until all coins are taken, and the winer is the person who takes the last coin.

Fernandes is very familiar with this game, and Li is also very clever. So you can assume that both of them know the best strategy to win the game. Now we know the situation at the beginning, and that Fernandes takes coins first. The question is who will win the game?

Input
The first line of the input is a single integer T, representing the number of test cases. Then the description of these T test cases follows.

The first line of each test cases has two integers: N and K, and in the second line there are N positive integers P1, P2, ..., PN givin the number of coins in each pile at the beginning.

1 ≤ N ≤ 10000
0 ≤ Pi ≤ 2147483647

Output
For each test case, if Fernandes can win the game, output "Fernandes wins"; otherwise output "Li wins" in a single line.

Sample Input
3
15 4
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 1
4 12 8
3 2
23 12 8

Sample Output
Li wins
Li wins
Fernandes wins

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Age of the Great Voyages
Problem Description "Age of the Great Voyages", which is also called "Uncharted Waters", is an old PC-game telling an interesting story in the period between the 15-th century and the 17-th century, when European explorers sailed the seas to open new alternative ways to Asia when the Ottoman Empire blocked the land routes. The story evolves on the search of the seven "Proof of the Conqueror", which are seven ancient artifacts, in seven areas around the world (Northern Europe, Mediterranean, Africa, New World, Indian Ocean, South Asia and East Asia). It is said that having these proofs proves that the sailor is the champion of all sailors. Four sailors unwittingly involved in the struggle of the quest of the search of the Proof of the Conqueror. - from wikipedia Li Huamei, an Admiral of Ming Dynasty, is one of the four protagonists in the story. She trys to find the "Proof of the Conqueror" for the revitalization of the motherland. One person's power is limited, so she searches for like-minded people to help her. When Li's fleet voyages to the New World, she meets an intelligent man - Fernandes and invite him to become a member of the fleet as a staff officer. While Fernandes is a strange man, he requires that he will join only if Li can win in the following game: At the beginning, there are N piles of coins on the desk, the i-th pile has Pi coins. Then Fernandes and Li take turns to take coins from those piles on the desk according to the following rule: when it is someone's turn to take coins, at first, he/she has to select no more than K (and no less than 1) piles that still have coins arbitrarily, then take arbitrary number (at least 1) of coins from each piles he/she selects. The game is over until all coins are taken, and the winer is the person who takes the last coin. Fernandes is very familiar with this game, and Li is also very clever. So you can assume that both of them know the best strategy to win the game. Now we know the situation at the beginning, and that Fernandes takes coins first. The question is who will win the game? Input The first line of the input is a single integer T, representing the number of test cases. Then the description of these T test cases follows. The first line of each test cases has two integers: N and K, and in the second line there are N positive integers P1, P2, ..., PN givin the number of coins in each pile at the beginning. 1 ≤ N ≤ 10000 0 ≤ Pi ≤ 2147483647 Output For each test case, if Fernandes can win the game, output "Fernandes wins"; otherwise output "Li wins" in a single line. Sample Input 3 15 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 4 12 8 3 2 23 12 8 Sample Output Li wins Li wins Fernandes wins
Columbus’s bargain 的问题
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Columbus's bargain
Description On the evening of 3 August 1492, Christopher Columbus departed from Palos de la Frontera with a few ships, starting a serious of voyages of finding a new route to India. As you know, just in those voyages, Columbus discovered the America continent which he thought was India. Because the ships are not large enough and there are seldom harbors in his route, Columbus had to buy food and other necessary things from savages. Gold coins were the most popular currency in the world at that time and savages also accept them. Columbus wanted to buy N kinds of goods from savages, and each kind of goods has a price in gold coins. Columbus brought enough glass beads with him, because he knew that for savages, a glass bead is as valuable as a gold coin. Columbus could buy an item he need only in four ways below: Pay the price all by gold coins. Pay by ONE glass bead and some gold coins. In this way, if an item's price is k gold coins, Columbus could just pay k - 1 gold coins and one glass bead. Pay by an item which has the same price. Pay by a cheaper item and some gold coins. Columbus found out an interesting thing in the trade rule of savages: For some kinds of goods, when the buyer wanted to buy an item by paying a cheaper item and some gold coins, he didn't have to pay the price difference, he can pay less. If one could buy an item of kind A by paying a cheaper item of kind B plus some gold coins less than the price difference between B and A, Columbus called that there was a "bargain" between kind B and kind A. To get an item, Columbus didn't have to spend gold coins as many as its price because he could use glass beads or took full advantages of "bargains". So Columbus wanted to know, for any kind of goods, at least how many gold coins he had to spend in order to get one - Columbus called it "actual price" of that kind of goods. Just for curiosity, Columbus also wanted to know, how many kinds of goods are there whose "actual price" was equal to the sum of "actual price" of other two kinds. Input There are several test cases. The first line in the input is an integer T indicating the number of test cases (0 < T <= 10). For each test case: The first line contains an integer N, meaning there are N kinds of goods (0 < N <= 20). These N kinds are numbered from 1 to N. Then N lines follow, each contains two integers Q and P, meaning that the price of the goods of kind Q is P. (0 < Q <= N, 0 < P <= 30) The next line is a integer M (0 < M <= 20), meaning there are M "bargains". Then M lines follow, each contains three integers N1, N2 and R, meaning that you can get an item of kind N2 by paying an item of kind N1 plus R gold coins. It's guaranteed that the goods of kind N1 is cheaper than the goods of kind N2 and R is none negative and less than the price difference between the goods of kind N2 and kind N1. Please note that R could be zero. Output For each test case: Please output N lines at first. Each line contains two integers n and p, meaning that the "actual price" of the goods of kind n is p gold coins. These N lines should be in the ascending order of kind No.. Then output a line containing an integer m, indicating that there are m kinds of goods whose "actual price" is equal to the sum of "actual price" of other two kinds. Sample Input 1 4 1 4 2 9 3 5 4 13 2 1 2 3 3 4 6 Sample Output 1 3 2 6 3 4 4 10 1
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