popFront causing more memory to be used

[ixid]

I'm not sure what's going on here. Using this code to solve a 
reddit programming challenge to return the Nth term of a 
Fibonacci-like sequence of arbitrary length:

    module main;
    import std.stdio, std.array, std.datetime;
    ulong f(int k, int n) {
        ulong[] nums = new ulong[k];
        nums[$ - 1] = 1;
        ulong total = 1;
        foreach(i;k..n + 1) {
            nums ~= total % 10^^8;
            total += nums[$ - 1] - nums[$ - k - 1];
            nums.popFront(); //The optional, trouble line
        }
        return nums[$ - 1];
    }

    void main() {
        StopWatch sw;
        sw.start;
        f(100, 10_000).writeln();
        f(3^^13, 5^^10).writeln;
        sw.peek.msecs.writeln("msecs");
    }

I assumed using popFront to keep the memory use in check would be 
the sensible thing to do but memory used goes from 170MB to 250MB 
when adding popFront. What's going on and how should I have built 
this data structure?