Monocarp has a deck of cards numbered from $$$1$$$ to $$$n$$$. Initially, the cards are arranged from smallest to largest, with $$$1$$$ on top and $$$n$$$ at the bottom.

Monocarp performed $$$k$$$ actions on the deck. Each action was one of three types:

remove the top card;
remove the bottom card;
remove either the top or bottom card.

Your task is to determine the fate of each card: whether it remains in the deck, has been removed, or might be both.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 2 \cdot 10^5$$$).

The second line contains a string $$$s$$$ of length $$$k$$$, consisting of characters 0, 1, and/or {2}. This string describes Monocarp's actions. If the $$$i$$$-th character is 0, Monocarp removes the top card on the $$$i$$$-th action. If it's 1, he removes the bottom card. If it's 2, either the top or bottom card can be removed.

Additional constraint on the input: the sum of $$$n$$$ over all test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print a string consisting of $$$n$$$ characters. The $$$i$$$-th character should be + (plus sign) if the $$$i$$$-th card is still in the deck, - (minus sign) if it has been removed, or ? (question mark) if its state is unknown.

Deck of Cards

Examples