Lights Out

The cows so much prefer to sleep in the dark. Every night, though,
when they return to the barn, some of the L (3 <= L <= 50) lights
are switched on. They know the location of the push button switches
but, as is always the problem, they lack fingers. The buttons are
arranged in a nice row, and the left most button (#1) toggles light
#1; the next button to the right toggles light #2; and so on.
('Toggle' means change from off-to-on or on-to-off, depending on
the current state of the switch.)

They do however have an unusual pitchfork with T (1 <= T <= 7)
slots, each one of which might hold a tine that can push the switches.
Some tines are present; some might be absent. By way of example,
imagine a pitchfork with T=4 and a missing tine. This particular
pitchfork has tines in the 1st, 2nd, and 4th positions, easily
described as '1101'.

If the pitchfork is aimed at the leftmost switch, then lights #1,
#2, and #4 are toggled (#3 isn't toggled since there is no tine
there). If the pitchfork is aimed at switch #3, then lights #3, #4,
and #6 are toggled. The pitchfork must be aimed so that all its
tine slots touch switches; the fork cannot cross the end of the line of
switches.

Given a list of lights that are on and a configuration for a
pitchfork, determine a sequence of pitchfork presses that will
toggle the lights until the minimum number of lights is lit.

PROBLEM NAME: xlite

INPUT FORMAT:

* Line 1: Two space-separated integers: L and T

* Line 2: A line with L characters (and no spaces), each of which is
        '0' or '1'. '1' means a light in that slot is lit; '0' means
        the light in that slot is not lit.

* Line 3: A line with T characters, each of which is '0' or '1' (no
        spaces are present). '1' means a tine is present on the
        pitchfork in that slot; '0' means otherwise.  The pitchfork
        can not be inverted.

SAMPLE INPUT:

10 4
1111111111
1101

INPUT DETAILS:

All 10 lights all on; three of four tines are present on the pitchfork
(tine #3 is missing)

OUTPUT FORMAT:

* Line 1: K, the number of positions at which the pitchfork was aimed.


SAMPLE OUTPUT:

5


OUTPUT DETAILS:

1111111111  Start
1100101111  Toggle 3
0001101111  Toggle 1
0000000111  Toggle 4
0000001010  Toggle 7
0000010000  Toggle 6
One light remaining is the best one can do.  Many other solutions
will leave one light lit (possibly a different light).