Problem: We have N points in a two-dimensional plane.
The coordinates of the i-th point (1 \leq i \leq N) are (x_i,y_i).
Let us consider a rectangle whose sides are parallel to the coordinate axes that contains K or more of the N points in its interior.
Here, points on the sides of the rectangle are considered to be in the interior.
Find the minimum possible area of such a rectangle.

Constraints

* 2 \leq K \leq N \leq 50
* -10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)
* x_i≠x_j (1 \leq i<j \leq N)
* y_i≠y_j (1 \leq i<j \leq N)
* All input values are integers. (Added at 21:50 JST)

Input

Input is given from Standard Input in the following format:


N K
x_1 y_1
:
x_{N} y_{N}


Output

Print the minimum possible area of a rectangle that satisfies the condition.

Examples

Input

4 4
1 4
3 3
6 2
8 1


Output

21


Input

4 2
0 0
1 1
2 2
3 3


Output

1


Input

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999


Output

3999999996000000001

Solution (in PYTHON3):

Solution:
N, K = map(int, input().split())
x = [None] * N
y = [None] * N

for i in range(N):
    x[i], y[i] = map(int, input().split())

ans = 10**20
sx = sorted(x)
sy = sorted(y)
# 長方形の辺の位置で全探索
for i in range(N):# 左
    for j in range(i+1,N):# 右
        for k in range(N):# 上
            for l in range(k+1,N):# 下
                count = 0
                # 点が長方形に含まれるか確認
                for m in range(N):
                    if sx[i] <= x[m] <= sx[j] and sy[k] <= y[m] <= sy[l]:
                        count += 1
                if count >= K:
                    ans = min(ans, (sx[j]-sx[i]) * (sy[l]-sy[k]))
print(ans)