Problem:
Score : 200 points

Problem Statement

There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.
During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.
That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.
The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.
Find the earliest possible time to reach coordinate X.

Constraints

X is an integer.

1≤X≤10^9

Input

The input is given from Standard Input in the following format:

X

Output

Print the earliest possible time for the kangaroo to reach coordinate X.

Sample Input 1

6

Sample Output 1

3

The kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.

Sample Input 2

2

Sample Output 2

2

He can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.

Sample Input 3

11

Sample Output 3

5

Solution in PyPy3 (2.4.0) (judge verdict: Runtime Error)

# -*- coding: utf-8 -*-
def inpl(): return list(map(int, input().split()))
from copy import deepcopy
from operator import add
from itertools import accumulate

N, K = inpl()
A = sorted(inpl())
S = list(accumulate(A, add))
A = A[::-1]
DP = [False for _ in range(K)]
DP[0] = 1
OK = [False for _ in range(N)]

for i, a in enumerate(A):
    DP0 = deepcopy(DP)
    if a >= K:
        OK[i] = True
        continue
    for j, d in enumerate(DP0[-S[::-1][i]:], max(0, K-S[::-1][i])):
        if d:
            if j + a >= K:
                OK[i] = True
                break
            else:
                DP[j+a] = True

if sum(OK) == 0:
    print(N)
else:
    print(OK[::-1].index(True))