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문제

Soundex is a phonetic algorithm for transforming a string into a code, which is always a letter followed by three digits. The purpose is that strings with a different spelling but similar pronounciation will be transformed into the same code. The transformation rules are as follows:

  • The first letter of the string is the first letter of the code.
  • Subsequent consonants are replaced by digits:
    • b, f, p, v with 1
    • c, g, j, k, q, s, x, z with 2
    • d, t with 3
    • l with 4
    • m, n with 5
    • r with 6
  • h and w are ignored. The vowels, a, e, i, o, u and y, are not encoded.
  • Two or more adjacent letters with the same digit are replaced with a single digit. Two or more letters with the same digit separated with h or w are also replaced by a single digit. Two letters with the same digit separated by a vowel will appear as the digit twice.
  • Repeat the previous step until it isn’t possible to replace repeating digits with one digit.
  • If the resulting code has less than 3 digits, pad the end with zeroes until the code has 3 digits. If there are more than 3 digits, drop the rightmost digits.

Some example transformations are:

  • Both robert and rupert are transformed to R163.
  • baawwwww is transformed to B000.
  • hopp is transformed to H100. The first letter of the string always becomes the first letter in the code, even if it is a vowel or h or w.
  • ratatata is transformed to R333, because the vowel between each pair of t (3) forces the digit to be repeated.
  • yhhhwthwhtwhthwhwth is transformed to X300. All occurrences of h and w are ignored, leaving only one 3 in the code.
  • bbpb is transformed to B100. The first b is kept separate from the last three b’s. The remaining b’s are consecutive and are replaced with one digit.

Your evil friend Halvor has noticed that a lot of different words will give the same soundex code. For example, the strings rhhhbm, rubeno, rpowam, robnew and 73908 other strings with 6 or less letters will be converted to the code R150. This makes him very curious, and he wants to know the number of strings of the a given length or shorter that will be converted to the same soundex code. Naturally, he wants you to write a computer program to accomplish this task. Your friend does not care about upper or lower case, so AA, Aa, aa etc are considered to be equal strings and should only be counted once.

입력

The first line of input contains a single integer T, the number of test cases to follow. Each test case begins with a line containing a string S and an integer number L. S represents a soundex code, and consists of one uppercase letter followed by three digits. L represents the maximum length of the original string which is converted into the given soundex code.

  • 0 < T ≤ 100
  • 0 < L ≤ 1000
  • All soundex codes will start with an uppercase letter.
  • Two strings S and T are equal if they have the same length and the letters si, ti at each position are equal, regardless of case.
  • Only letters between a and z are considered. No æ, ø, å or other non-English characters are to be used.
  • The soundex code is always legal. That is, a non-zero digit will never follow a zero digit, and the digits range from 0 to 6.

출력

For each test case output one line containing a single number, the number of strings of length L or less having the soundex code S. This number can be large, so output it modulo 1,000,000,007.

예제 입력

3
A300 2
R150 6
X123 1

예제 출력

2
73912
0

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