Why is the loop running infinitely?

In the following code snippet, I intended to exit the while loop when the value of m becomes 0 or less than 0. But my while loop is still running even after the value of m finally decrements to 0. What is the reason for this infinite loop? Does it have anything to do with my else statement? If it does, why so?

NOTE: The reason I need the while loop here is because I need the for loop to run afresh when it terminates but the value of m is greater than 0.

Here is my code:

n, m = input().split()
n = int(n)
m = int(m)

while m>=0:
    for i in range(n+1):
        if m >= i:
            m -= i
        else:
            break
   
        
print(m)

>Solution :

This is solved more clearly by recursion. Imagine a function f that determines how many chips are left to the presenter:

def f(chips: int, walruses: int, position: int = 1) -> int:
    # Base case, there are fewer chips than the current position number
    if chips < position:
        return chips
    else:  # Iterative case; decrement chips and recalculate position
        chips = chips - position
        position = position + 1 if position < walruses else 1
        return f(chips, walruses, position)

walrus_count, starting_chips = input().split()
print(f(int(starting_chips), int(walrus_count)))

That said, if you really want to use a while loop:

def f(chips: int, walruses:int) -> int:
    position = 1
    # Quit if we don't have enough chips
    while chips > position:
        # Decrement chips
        chips = chips - position
        # Reset position if we've gone around the circle
        position = 1 if position >= walruses else position + 1
    return chips

The problem you are having is that you’re nesting loops.

while m >= 0: # Loop until you run out of chips -> but that is not what the problem calls for
    for i in range(0, n+1):  # i is position, and you're looking to loop once you run out of walruses. Alas, you're zero-indexing here!
        if m >= i:  # Check to see if there are enough chips, which is a half-overlap of the outer loop
            m -= i  # Decrement chips, correct
        else:
            break  # Breaks out of for-loop, but not while-loop
     # No extra check here to see if you need to break out of while loop. Need to add one, or fix the while loop check.