Problem:
Score : 300 points

Problem Statement

There are N candles placed on a number line.
The i-th candle from the left is placed on coordinate x_i.
Here, x_1 < x_2 < ... < x_N holds.

Initially, no candles are burning.
Snuke decides to light K of the N candles.

Now, he is at coordinate 0.
He can move left and right along the line with speed 1.
He can also light a candle when he is at the same position as the candle, in negligible time.

Find the minimum time required to light K candles.

Constraints

1 \leq N \leq 10^5

1 \leq K \leq N

x_i is an integer.

|x_i| \leq 10^8

x_1 < x_2 < ... < x_N

Input

Input is given from Standard Input in the following format:

N K
x_1 x_2 ... x_N

Output

Print the minimum time required to light K candles.

Sample Input 1

5 3
-30 -10 10 20 50

Sample Output 1

40

He should move and light candles as follows:

Move from coordinate 0 to -10.

Light the second candle from the left.

Move from coordinate -10 to 10.

Light the third candle from the left.

Move from coordinate 10 to 20.

Light the fourth candle from the left.

Sample Input 2

3 2
10 20 30

Sample Output 2

20

Sample Input 3

1 1
0

Sample Output 3

0

There may be a candle placed at coordinate 0.

Sample Input 4

8 5
-9 -7 -4 -3 1 2 3 4

Sample Output 4

10

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
from bisect import bisect_left
def input(): return sys.stdin.readline().strip()


def main():
    N, K = map(int, input().split())
    X = list(map(int, input().split()))
    X.sort()
    idx = bisect_left(X, 0)
    #print("idx={}".format(idx))
    ans = 10**10
    if idx == N:
        print(-X[-K])
        return
    elif 0 == X[idx]:
        for i in range(idx + 1):
            num = idx - i + 1
            if num > K: continue
            elif num == K: ans = min(ans, -X[i])
            elif 0 <= idx + (K - num) and idx + (K - num) < N:
                ans = min(ans, -2 * X[i] + X[idx + (K - num)])
        for i in range(idx + 1, N):
            num = i - idx + 1
            if num > K: continue
            elif num == K: ans = min(ans, X[i])
            elif 0 <= idx - (K - num) and idx - (K - num) < N:
                ans = min(ans, 2 * X[i] - X[idx - (K - num)])
    else:
        for i in range(idx):
            num = idx - i
            if num > K: continue
            elif num == K: ans = min(ans, -X[i])
            elif 0 <= idx + (K - num) - 1 and idx + (K - num) - 1 < N:
                ans = min(ans, -2 * X[i] + X[idx + (K - num) - 1])
            #print("i={}, num={}, cand={}, ans={}".format(i, idx - (K - num) - 1, -2 * X[i] + X[idx + (K - num) - 1], ans))
        for i in range(idx, N):
            num = i - idx + 1
            if num > K: continue
            elif num == K: ans = min(ans, X[i])
            elif 0 <= idx - (K - num) and idx - (K - num) < N:
                ans = min(ans, 2 * X[i] - X[idx - (K - num)])
            #print("i={}, ans={}".format(i, ans))
    print(ans)

if __name__ == "__main__":
    main()