did modular exponentiation with high level of ignorance (mooooooooo tablet, see problem F)

modular_exponentiation.py

@@ -3,10 +3,24 @@ import sys
 
 def mod_exp(x, y, m):
     k = x % m
-    for i in range(y):
-        print(i)
-        k = (k * x) % m
-    return k
+    results = {}
+    return exp_m(results, k, y, m)
+
+def exp_m(results, k, y, m):
+    if y in results:
+        return results[y]
+    else:
+        if k == 1:
+            ret = 1
+        elif y == 0:
+            ret = 1
+        elif y == 1:
+            ret = k
+        else:
+            h = y // 2
+            ret = (exp_m(results, k, h, m) % m * exp_m(results, k, y - h, m) % m) % m
+        results[y] = ret
+        return ret
 
 line = sys.stdin.readline().split()
 x = int(line[0])