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 PyPy2 (5.6.0) (judge verdict: Runtime Error)

n,k=map(int,raw_input().split())
a=map(int,raw_input().split())
a.sort()
used=[False]*n
idx=n-1
cnt=0
while True:
    if idx-cnt<0:
        break
    tmp=sum(a[idx-cnt:idx+1])
    if tmp<k:
        cnt+=1
        continue
    for i in xrange(idx-cnt,idx+1):
        used[i]=True
    tmp-=a[idx-cnt]
    for i in xrange(idx-cnt-1,-1,-1):
        if tmp+a[i]>=k:
            used[i]=True
        else:
            break
    idx-=1
    cnt=0
ans=0
for i in xrange(n):
    if not used[i]:
        ans+=1
print ans