레이팅 미적용You may know that March 14 is known as “\(\pi\)-day”, since \(3.14\) (which is the third month and
fourteenth day) is a good approximation of \(\pi\).
Mathematicians celebrate this day by eating pie.
Suppose that you have \(n\) pieces
of pie, and \(k\) people who are lined
up for pieces of pie. All \(n\) pieces
of pie will be given out. Each person will get at least one piece of
pie, but mathematicians are a bit greedy at times. So, they always get
at least as many of pieces of pie as the person in front of them.
For example, if you have 8 pieces of pie and \(4\) people in line, you could give out
pieces of pie in the following five ways (with the first person in line
being the first number in the list): \([1,1,1,5]\), \([1,1,2,4]\), \([1,1,3,3]\), \([1,2,2,3]\), \([2,2,2,2]\).
Notice that if \(k=n\), there is
only one way to give out the pieces of pie: every person gets exactly
one piece. Also, if \(k=1\), there is
only one way to give out the pieces of pie: that single person gets all
the pieces.
Write a program that determines the number of ways that the pieces of
pie can be given out.
The first line of input is the integer number of pieces of pie, \(n\) \((1 \leq n \leq 250)\).
The second line of input is the integer \(k\) which is the number of people in line
\((1 \leq k \leq n)\).
For at least 20% of the marks for this problem, \(n \leq 9\). For at least 50% of the marks
for this problem, \(n \leq 70\). For at
least 85% of the marks for this problem, \(n \leq 120\).
The output will consist of a single integer which is the number of
ways that the pieces of pie can be distributed. The output is guaranteed
to be less that \(2^{31}\).
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