A logistics hub stamps every shipping container with a lowercase seal code. A container's seal strength is defined as the number of times the alphabetically earliest letter appearing anywhere in its code occurs in that code — for instance, the code bbto has alphabetically earliest letter b, which occurs twice, so its seal strength is 2; the code z has seal strength 1.

The hub keeps a reference vault holding the codes of n2 previously logged containers. A new batch of n1 incoming shipment codes has just arrived at the gate, and for every incoming code the inspector wants to know exactly how many vault codes have a seal strength that is strictly greater than that incoming code's own seal strength.

Input format

• Line 1: two integers n1 and n2.
• Line 2: n1 space-separated lowercase strings — the incoming shipment codes, in order.
• Line 3: n2 space-separated lowercase strings — the vault codes.

Output format

Print n1 integers separated by single spaces on one line. The i-th integer is the number of vault codes whose seal strength is strictly greater than the seal strength of the i-th incoming shipment code.

Constraints

• 1 <= n1, n2 <= 2000
• Each code has length between 1 and 10 inclusive, and consists only of lowercase English letters a-z.

2 4
cargo seal
bin zoo aabb dock

2 2

2 4
xyz aab
aaa bb xyz aabbcc

3 1