Process pod logs with global increments and pop-min

Problem Statement

You are monitoring logs from multiple pods. Each pod has a counter representing the number of processed requests, initially set to 0. You need to implement a data structure that supports the following operations:

1. increment(k, val): Increase the counter of pod k by val.
2. global_increment(val): Increase the counters of all existing pods by val.
3. pop_min(): Remove and return the pod ID with the smallest counter value. If there is a tie, return the one with the smallest ID. If multiple pods have the same minimum, remove one.

Constraints

• Number of pods N up to 10^5.
• Number of operations M up to 10^5.
• val is a non-negative integer.

Interface

class PodManager:
    def __init__(self, pod_ids):
        # Initialize all pods with counter 0
        pass

    def increment(self, pod_id, val):
        pass

    def global_increment(self, val):
        pass

    def pop_min(self):
        pass

Example

# Initialize with pods [1, 2]
manager = PodManager([1, 2])
manager.increment(1, 10)
manager.global_increment(5)
# Pod 1: 15, Pod 2: 5
manager.pop_min() # returns 2
manager.pop_min() # returns 1