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.

Incorrect submission (verdict: Wrong Answer):
n, k = map(int, input().split())
XY = [list(map(int, input().split())) for _ in range(n)]
XY.sort(key=lambda x: x[0])
XY = [xy + [x] for x, xy in enumerate(XY)]
XY.sort(key=lambda x: x[1])
XY = [xy + [y] for y, xy in enumerate(XY)]

gr = [[0] * n for _ in range(n)]
for _, _, i, j in XY:
  gr[i][j] = 1

rui = [[0] * (n + 1) for _ in range(n + 1)]
for i in range(n):
  for j in range(n):
    rui[i + 1][j + 1] = rui[i + 1][j] + rui[i][j + 1] - rui[i][j] + gr[i][j]


ans = 10 ** 19
for i in range(n - 1):
  for j in range(i + 1, n):
    x = [XY[i][0] for i in range(2)]
    y = [XY[i][1] for i in range(2)]
    ii = [XY[i][2] for i in range(2)]
    jj = [XY[i][3] for i in range(2)]
    innerPoints = rui[max(ii)+1][max(jj)+1] \
                + rui[min(ii)][min(jj)] \
                - rui[min(ii)][max(jj)] \
                - rui[max(ii)][min(jj)]
    if innerPoints >= k:
      area = (max(x) - min(x)) * (max(y) - min(y)) 
      if area < ans:
        ans = area

if n > 2:
  for i in range(n - 2):
    for j in range(i + 1, n - 1):
      for k in range(j + 1, n):
        x = [XY[i][0] for i in range(3)]
        y = [XY[i][1] for i in range(3)]
        ii = [XY[i][2] for i in range(3)]
        jj = [XY[i][3] for i in range(3)]
        innerPoints = rui[max(ii)+1][max(jj)+1] \
                    + rui[min(ii)][min(jj)] \
                    - rui[min(ii)][max(jj)] \
                    - rui[max(ii)][min(jj)]
        if innerPoints >= k:
          area = (max(x) - min(x)) * (max(y) - min(y)) 
          if area < ans:
            ans = area

if n > 3:
  for i in range(n - 3):
    for j in range(i + 1, n - 2):
      for k in range(j + 1, n - 1):
        for l in range(k + 1, n):
          x = [XY[i][0] for i in range(4)]
          y = [XY[i][1] for i in range(4)]
          ii = [XY[i][2] for i in range(4)]
          jj = [XY[i][3] for i in range(4)]
          innerPoints = rui[max(ii)+1][max(jj)+1] \
                      + rui[min(ii)][min(jj)] \
                      - rui[min(ii)][max(jj)] \
                      - rui[max(ii)][min(jj)]
          if innerPoints >= k:
            area = (max(x) - min(x)) * (max(y) - min(y)) 
            if area < ans:
              ans = area

print(ans)

Fixed, accepted submission:
n, k = map(int, input().split())
XY = [list(map(int, input().split())) for _ in range(n)]
XY.sort(key=lambda x: x[0])
XY = [xy + [x] for x, xy in enumerate(XY)]
XY.sort(key=lambda x: x[1])
XY = [xy + [y] for y, xy in enumerate(XY)]

gr = [[0] * n for _ in range(n)]
for _, _, i, j in XY:
  gr[i][j] = 1
  
rui = [[0] * (n + 1) for _ in range(n + 1)]
for i in range(n):
  for j in range(n):
    rui[i + 1][j + 1] = rui[i + 1][j] + rui[i][j + 1] - rui[i][j] + gr[i][j]
    

ans = 10 ** 21
for i in range(n - 1):
  for j in range(i + 1, n):
    x = [XY[m][0] for m in [i, j]]
    y = [XY[m][1] for m in [i, j]]
    ii = [XY[m][2] for m in [i, j]]
    jj = [XY[m][3] for m in [i, j]]
    innerPoints = rui[max(ii) + 1][max(jj) + 1] \
                + rui[min(ii)][min(jj)] \
                - rui[min(ii)][max(jj) + 1] \
                - rui[max(ii) + 1][min(jj)]
    if innerPoints >= k:
      area = (max(x) - min(x)) * (max(y) - min(y)) 
      if area < ans:
        ans = area

if n > 2:
  for i in range(n - 2):
    for j in range(i + 1, n - 1):
      for l in range(j + 1, n):
        x = [XY[m][0] for m in [i, j, l]]
        y = [XY[m][1] for m in [i, j, l]]
        ii = [XY[m][2] for m in [i, j, l]]
        jj = [XY[m][3] for m in [i, j, l]]
        innerPoints = rui[max(ii) + 1][max(jj) + 1] \
                    + rui[min(ii)][min(jj)] \
                    - rui[min(ii)][max(jj) + 1] \
                    - rui[max(ii) + 1][min(jj)]
        if innerPoints >= k:
          area = (max(x) - min(x)) * (max(y) - min(y)) 
          if area < ans:
            ans = area

if n > 3:
  for i in range(n - 3):
    for j in range(i + 1, n - 2):
      for l in range(j + 1, n - 1):
        for o in range(l + 1, n):
          x = [XY[m][0] for m in [i, j, o, l]]
          y = [XY[m][1] for m in [i, j, o, l]]
          ii = [XY[m][2] for m in [i, j, o, l]]
          jj = [XY[m][3] for m in [i, j, o, l]]
          innerPoints = rui[max(ii) + 1][max(jj) + 1] \
                      + rui[min(ii)][min(jj)] \
                      - rui[min(ii)][max(jj) + 1] \
                      - rui[max(ii) + 1][min(jj)]
          if innerPoints >= k:
            area = (max(x) - min(x)) * (max(y) - min(y)) 
            if area < ans:
              ans = area

print(ans)