Binary string restoration

Consider a string of length $n$ made only of the characters 0 and 1. It has exactly $n - 1$ pairs of adjacent characters, and each pair is one of 00, 01, 10, 11.

You are given four integers $a$, $b$, $c$, $d$. Restore a string in which exactly $a$ adjacent pairs are 00, exactly $b$ are 01, exactly $c$ are 10, and exactly $d$ are 11. Its length is always $n = a + b + c + d + 1$.

Several strings can satisfy the counts, so print the lexicographically smallest one. All candidates have the same length, so comparing them character by character from the first position is enough.

The first line contains the number of tests $t$ ($1 \le t \le 10000$).

Each of the next $t$ lines contains four integers $a$, $b$, $c$, $d$ ($0 \le a, b, c, d \le 20$) separated by spaces. In every test $a + b + c + d \ge 1$.

Print $t$ lines. For each test print the lexicographically smallest string that satisfies the counts. If no string satisfies them, print impossible.