Maximum and Minimum Precipitation in Consecutive Days

In this problem, you are given the precipitation amounts for n days. Your task is to compute the maximum and minimum total precipitation that occurred over exactly k consecutive days. Formally, given an integer ( n ) and an integer ( k ), along with a list ( P = [p_1, p_2, \dots, p_n] ) of precipitation amounts, you should find:

[ max = \max_{1 \leq i \leq n-k+1} \sum_{j=i}^{i+k-1} p_j, \quad min = \min_{1 \leq i \leq n-k+1} \sum_{j=i}^{i+k-1} p_j. ]

The input is provided via standard input and the output should be printed to standard output. This problem requires a sliding window technique to efficiently compute the sum over every contiguous block of ( k ) days.

inputFormat

The first line of input contains two integers ( n ) and ( k ) separated by a space, where ( n ) is the total number of days and ( k ) is the number of consecutive days to consider. The second line contains ( n ) space-separated integers, representing the precipitation amounts for each day.

outputFormat

Output two space-separated integers: the maximum and the minimum total precipitation over any segment of exactly ( k ) consecutive days.## sample

7 3
2 1 5 7 9 3 4

21 8