Statement

You oversee N Internet-of-Things (IoT) devices arranged on a ring of M residues. The devices are numbered from 0 to N - 1. Each device displays a phase represented by an integer between 0 and M - 1 (inclusive). The initial phase of device i is A_i. Your goal is to make all devices display the same phase. To achieve this, you may repeatedly broadcast an instruction of the form "bump r". This instruction causes every device whose current phase is exactly r to shift to phase (r + 1) \bmod M. Find a sequence of instructions with the minimum possible length that makes every device display the same phase.