Magical Mod Arena - Fast Power with Modulo

🔮 Power Calculation

210 mod 1000

📊 Exponent in Binary (process right to left)

Base (a)

Exponent (b)

Modulo (m)

📚 Binary Exponentiation (Fast Power)

Calculate a^b mod m in O(log b) time using bit manipulation!

          result = 1 while (exp > 0): if (exp & 1): // If last bit is 1 result =
          (result * base) % mod base = (base * base) % mod // Square exp = exp
          >> 1 // Right shift (divide by 2)
        

Key insight: Any number can be expressed as sum of powers of 2.
Example: 2¹⁰ = 2⁸ × 2² (since 10 = 1010 in binary)