Choose Your Own Arithmetic

In Waterloo you have probably seen a goose or two. But how do you make geese appear on a calculator? Start with $6$, add $7$, multiply by $6$, multiply by $8$, add $7$, multiply by $8$, and multiply by $7$. You get $35336$. Flip the calculator upside down and it spells gEESE:

You want a program that builds tricks like this automatically. The trouble is that your calculator has many broken buttons: the only operators that still work are $+$ and $\times$, and only some of the digit keys respond. Given a target number, decide whether your half-broken calculator can reach it using single-digit inputs and a fixed number of operations.

Note: the calculator applies each operation the instant it is entered and ignores the usual order of operations. For example, $2 + 3 \times 4$ is evaluated left to right as $(2 + 3) \times 4 = 20$, not $2 + 12 = 14$.

The first line contains $W$, the exact number of operations you must perform ($0 \le W \le 6$).

The second line contains $D$, the number of working digit keys ($1 \le D \le 10$).

Each of the next $D$ lines contains one working digit. These digits are distinct integers from $0$ to $9$.

The next line contains $V$, the number of target values ($1 \le V \le 5$).

Each of the following $V$ lines contains one integer between $0$ and $5000000$ inclusive: a value you would like your calculator to show.

Print $V$ lines, one per target value. For each target print Y if it can be reached and N if it cannot, using exactly $W$ operations with the $D$ available digits.

Formally, a target $T$ is reachable if you can begin with one of the $D$ digits and then, by adding or multiplying by one of the digits exactly $W$ times, end at $T$. Digits may be reused and you do not have to use all of them. You may never enter a multi-digit number.