implement keypad

src/utils.py

@@ -0,0 +1,7 @@
+from math import factorial, comb
+
+def total_valid_nkode_states(k: int, p: int) -> int:
+   return factorial(k) ** (p-1)
+
+def total_shuffle_states(k: int, p: int) -> int:
+    return comb(p, p // 2) * factorial(k)