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 Problem Statement for KitayutaMart

Problem Statement


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Kitayuta Mart is the largest supermarket in Shuseki Kingdom, offering a great variety of food and household products. The main products are fruits, especially apples. The store sells K kinds of apples, numbered from 1 to K. The price system is a little special: the original price of an apple of kind i (1 <= i <= K) is i yen (the currency of the kingdom). However, if a customer wants to buy more than one apple of kind i, the second apple will cost 2*i yen, the third apple will cost 22*i yen, and so on. In general, if a customer is buying n apples of kind i, the actual price of the j-th (1 <= j <= n) apple will be 2j-1*i yen. The store has a sufficient supply of each kind of apples.

Lun the dog loves apples. She wants to buy N apples at Kitayuta Mart. The kinds of apples does not matter to her, thus she will choose N apples so that the total price calculated using the above formula is minimized. You are given two ints: N and K. Find and return the actual price (NOT the original price) of the apple with the highest actual price among the apples that she will buy modulo 1,000,000,007.



Parameters:int, int
Method signature:int lastPrice(int N, int K)
(be sure your method is public)


-It can be shown that the answer is unique.


-N will be between 1 and 1,000,000,000, inclusive.
-K will be between 1 and 1,000,000,000, inclusive.


Returns: 4
The store sells only one kind of apples. Their original price is 1 yen. She will buy three of them, and the most expensive one will cost 22*1 = 4 yen.
Returns: 2
In this case, another kind of apples is also on sale. Instead of buying three of kind 1, she can buy two of kind 1 and one of kind 2. Their costs will be 1, 2, and 2 yen, so the most expensive apple in this case only costs 2 yen.
Returns: 4
This time, yet another kind of apples is available, and she needs five apples. There are two options:
  • two of kind 1, two of kind 2, one of kind 3
  • three of kind 1, one of kind 2, one of kind 3
In either way, she will have to pay 4 yen for the most expensive apple.
Returns: 570312504
In this extreme case, the price of an apple will reach 2999999999 yen.
Returns: 493827168

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This problem was used for:
       Single Round Match 648 Round 1 - Division I, Level Two