Amazon's database doesn’t support very large numbers, so numbers are stored as a string of binary characters, '0' and '1'. Accidentally, a '!' was entered at some positions and it is unknown whether they should be '0' or '1'.

The string of incorrect data is made up of the characters '0', '1', and '!' where '!' is the character that got entered incorrectly. '!' can be replaced with either '0' or '1'. Due to some internal faults, some errors are generated every time '0' and '1' occur together as '01' or '10' in any subsequence of the string. It is observed that the number of errors a subsequence '01' generates is xxx, while a subsequence '10' generates yyy errors.

Determine the minimum total errors generated. Since the answer can be very large, return it modulo 109+710^9 + 7109+7.

For example, given string errorString = "101!1", x=2x = 2x=2, y=3y = 3y=3:

Function Description

Complete the function getMinErrors in the editor below.

getMinErrors has the following parameter(s):

• string errorString: a string of characters '0', '1', and '!'
• int x: the number of errors generated for every occurrence of subsequence 01
• int y: the number of errors generated for every occurrence of subsequence 10

Returns

• int: the minimum number of errors possible, modulo 109+710^9 + 7109+7

Constraints

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