Let $s$ be some string consisting of symbols "0" or "1". Let's call a string $t$ a substring of string $s$, if there exists such number $1 \leq l \leq |s| - |t| + 1$ that $t = s_l s_{l+1} \ldots s_{l + |t| - 1}$. Let's call a substring $t$ of string $s$ unique, if there exist only one such $l$. 

For example, let $s = $"1010111". A string $t = $"010" is an unique substring of $s$, because $l = 2$ is the only one suitable number. But, for example $t = $"10" isn't a unique substring of $s$, because $l = 1$ and $l = 3$ are suitable. And for example $t =$"00" at all isn't a substring of $s$, because there is no suitable $l$.

Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols "0" and "1", the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him.

You are given $2$ positive integers $n$ and $k$, such that $(n \bmod 2) = (k \bmod 2)$, where $(x \bmod 2)$ is operation of taking remainder of $x$ by dividing on $2$. Find any string $s$ consisting of $n$ symbols "0" or "1", such that the length of its minimal unique substring is equal to $k$.


-----Input-----

The first line contains two integers $n$ and $k$, separated by spaces ($1 \leq k \leq n \leq 100\,000$, $(k \bmod 2) = (n \bmod 2)$).


-----Output-----

Print a string $s$ of length $n$, consisting of symbols "0" and "1". Minimal length of the unique substring of $s$ should be equal to $k$. You can find any suitable string. It is guaranteed, that there exists at least one such string.


-----Examples-----
Input
4 4

Output
1111
Input
5 3

Output
01010
Input
7 3

Output
1011011



-----Note-----

In the first test, it's easy to see, that the only unique substring of string $s = $"1111" is all string $s$, which has length $4$.

In the second test a string $s = $"01010" has minimal unique substring $t =$"101", which has length $3$.

In the third test a string $s = $"1011011" has minimal unique substring $t =$"110", which has length $3$.

Difficulty: competition

Starter code:

Solutions:
n,k=list(map(int,input().split()))

x=(n-(k-1)+1)//2
STR="0"*(x-1)+"1"

ANS=STR*(n//x+1)
print(ANS[:n])


n, k = [int(i) for i in input().split()]
print("1" * n if k == n else (("0" * ((n - k) // 2) + "1") * (n // ((n - k) // 2) + 1))[0:n])


def __starting_point():
    N, K = [int(x) for x in input().split()]
    len = (N - K) // 2 + 1
    s0 = '0' * (len - 1) + '1'
    print(s0 * (N // len) + s0[ : N % len])

__starting_point()

n, k = [int(i) for i in input().split()]
print((("0" * ((n - k) // 2) + "1") * (n // ((n - k) // 2 + 1) + 1))[:n])

n, k = map(int, input().split())
a = (n - k) // 2
s = '0' * a + '1'
print(s * (n // (a + 1)) + s[:n % (a + 1)])

n, k = list(map(int, input().split()))
if n == k:
    print("1" * n)
else:
    print((("0" * ((n - k + 2) // 2 - 1) + "1") * (n // ((n - k + 2) // 2) + 1))[:n])



n, k = map(int, input().split())
# while making the string, k = (n - 2 * length + 2)
length = (n - k + 2) // 2           # length of a cycle
string = "0" * (length - 1) + "1"   # make the cycle
answer = string * (n // length + 1) # make the string with length >= n
print(answer[ : n])

n,k=map(int,input().split())
print(((((n-k)//2)*"0"+"1")*(n//((n-k)//2+1)+1))[:n])

n,k=[int(x) for x in input().split()]
a=(n-k)//2
tot=''
for i in range(n):
    if (i+1)%(a+1)==0:
        tot+='1'
    else:
        tot+='0'
print(tot)


n, k = map(int, input().split())
if n == k:
    print("1" * n)
else:
    print((("0" * ((n - k + 2) // 2 - 1) + "1") * (n // ((n - k + 2) // 2) + 1))[:n])

n, k = map(int, input().split())

x = (n - k) // 2
f = ('0' * x) + '1'

f = f * ((n // (x+1)) + 1)
print(f[:n])

n,k = map(int,input().split())
if(n==k):
    print("1"*n)
    return
a = (n - k)>>1
i = 0
Ans = ""
while(i<n):
    Ans+="0" * (a)
    i+=a
    if(i>n-1):
        break
    Ans+="1" 
    i+=1
    if(i>n-1):
        break
print(Ans[:n])

import math
import sys
n, k = list(map(int, input().split()))
a = [0] * n
side = (n - k) // 2
for i in range(side, n, side + 1):
    a[i] = 1
print(''.join(map(str, a)))


n,k=list(map(int,input().split()))
e=(n-k)//2
c="0"*e+"1"
while(len(c)<=n):
    c=c+c
print(c[:n])