Certification#30
A mathematics teacher has prepared problems for certification, each involving the operations , , , and . Each problem contains a certain number of arithmetic operations. To pass certification, each student must solve problems selected from the list. The selection must be such that, in the chosen sequence, every subsequent problem (with a higher index in the list) contains more operations than the previous one.
Determine the number of different ways to select problems so that every such sequence satisfies the above condition.
The first line contains two integers and (1 \leq N \leq 100, 1 \leq K \leq 100), where is the number of problems prepared, and is the number required to pass certification.
The next lines each contain a single integer: the number of arithmetic operations in the -th problem. The number of operations in each problem does not exceed .
Output a single integer: the number of valid ways to choose problems according to the condition. Two ways are considered different if they differ by at least one problem. If there are no such ways, output -1.
Example 11