Ciphertext

Ivica studies cryptography, the science of encrypting messages so that only the intended recipient can read them. He found a method that turns a chosen digit Z into a record (the ciphertext) made of K zeros and ones. First, a key is chosen. The key is a sequence of K digits sorted in non-decreasing order. The digits do not have to be distinct. For example, when K=5, "01248", "12345", and "00122" are possible keys.

If the digit Z can be written as a sum of X digits that appear in the key, then the ciphertext gets a "1" at position i (counting from the left) when the i-th digit of the key (counting from the left) is one of the digits used in the sum. Otherwise the ciphertext gets a "0" at that position. If there are several possible ciphertexts for Z, all of them must be printed. Each digit of the key can be used in the sum at most once.

For example, let Z=8, K=5, X=2, and the chosen key be "01236". The required ciphertext is "00101", because 8 can be written as a sum of two digits from the key in only one way (2+6=8, "01236" gives "00101").

Write a program that, given the digit Z, the numbers K and X, and a key of length K, finds and prints the ciphertext or ciphertexts of Z as described above. The given digit can always be encrypted.

The first line contains the natural number K (1 ≤ K ≤ 20), the length of the key.

The second line contains the key, a sequence of K digits.

The third line contains the natural number X (1 ≤ X ≤ K).

The fourth line contains the digit Z (0 ≤ Z ≤ 9).

Print every ciphertext of the digit Z, one per line. The order of the output does not matter.

In the first test, "01247": 1+4=5, so the ciphertext is 01010.

In the second test, "001234": 0+2+4 gives 100101, 0+2+4 (using the other 0) gives 010101, and 1+2+3 gives 001110.