# USACO 2019 US Open Contest, Gold Problem 2. I Would Walk 500 Miles

Farmer John wants to divide his NN cows (N7500)(N≤7500), conveniently numbered 1N1…N, into KK non-empty groups (2KN2≤K≤N) such that no two cows from two different groups can interact with each other without walking some number of miles. Cow xx and Cow yy (where 1x<yN1≤x<y≤N) are willing to walk (2019201913x+2019201949y) mod 2019201997(2019201913x+2019201949y) mod 2019201997 miles to see each other.

Given a division of the NN cows into KK non-empty groups, let MM be the minimum of the number of miles any two cows in two different groups are willing to walk to see each other. To test the cows' devotion to each other, Farmer John wants to optimally divide the NN cows into KK groups such that MM is as large as possible. The memory limit for this problem is set to 512MB, above the usual 256MB limit.

#### INPUT FORMAT (file walk.in):

The input is just one line, containing NN and KK, separated by a space.

#### OUTPUT FORMAT (file walk.out):

Print out MM in an optimal solution.

#### SAMPLE INPUT:

3 2


#### SAMPLE OUTPUT:

2019201769


In this example, Cow 1 and Cow 2 are willing to walk 2019201817 miles to see each other. Cow 2 and Cow 3 are willing to walk 2019201685 miles. And Cow 1 and Cow 3 are willing to walk 2019201769 miles. Thus, by grouping the cows such that 1 is by herself and 2 and 3 are grouped together, M=min(2019201817,2019201769)=2019201769M=min(2019201817,2019201769)=2019201769 (which is the best we can do here).

Problem credits: Brian Dean

#### 中文版

Farmer John想要将他的编号为1N1…NNN头奶牛（N7500N≤7500）分为非空的KK组（2KN2≤K≤N），使得任意两头来自不同组的奶牛都需要走一定的距离才能相遇。奶牛xx和奶牛yy（其中1x<yN1≤x<y≤N）愿意为了见面走(2019201913x+2019201949y) mod 2019201997(2019201913x+2019201949y) mod 2019201997英里。

#### 输入样例：

3 2


#### 输出样例：

2019201769


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