input: def find_lcs(x: str, y: str) -> str:
      """
      Function to find the longest common subsequence of two strings.
      >>> find_lcs("abcdaf", "acbcf")
      'abcf'
      >>> find_lcs("AGGTAB", "GXTXAYB")
      'GTAB'
      """
output:     m, n = len(x), len(y)
      dp = [[0] * (n + 1) for _ in range(m + 1)]
      
      for i in range(1, m + 1):
          for j in range(1, n + 1):
              if x[i - 1] == y[j - 1]:
                  dp[i][j] = dp[i - 1][j - 1] + 1
              else:
                  dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
      
      lcs = []
      i, j = m, n
      while i > 0 and j > 0:
          if x[i - 1] == y[j - 1]:
              lcs.append(x[i - 1])
              i -= 1
              j -= 1
          elif dp[i - 1][j] > dp[i][j - 1]:
              i -= 1
          else:
              j -= 1
      
      return ''.join(reversed(lcs))