from bisect import bisect_right
from math import sqrt
class TestQueue:
    def __init__(self, n):
        self.n = n
        self.nn = int(sqrt(n))
        self.data = []
        self.index = []
        for i in range(1, n+1):
            ii = (i-1)//self.nn
            if ii == len(self.data):
                self.data.append([])
                self.index.append(i)
            self.data[-1].append(i)

    def solve(self, k):
        i = bisect_right(self.index, k)-1
        x = self.data[i].pop(k - self.index[i])
        for ii in range(i+1, len(self.index)):
            self.index[ii] -= 1
        if len(self.data[-1]) >= self.nn:
            self.data.append([])
            self.index.append(self.n)
        self.data[-1].append(x)
        if not self.data[i]:
            self.data.pop(i)
            self.index.pop(i)
        return x

queue = TestQueue(5)
print(queue.solve(5))
print(queue.solve(2))
print(queue.solve(3))
print(queue.solve(1))

queue = TestQueue(5)
print(queue.solve(5))
print(queue.solve(2))
print(queue.solve(3))
print(queue.solve(1))

5
2
4
1