Problem:
Score : 400 points

Problem Statement

The ABC number of a string T is the number of triples of integers (i, j, k) that satisfy all of the following conditions:

1 ≤ i < j < k ≤ |T| (|T| is the length of T.)

T_i = A (T_i is the i-th character of T from the beginning.)

T_j = B

T_k = C

For example, when T = ABCBC, there are three triples of integers (i, j, k) that satisfy the conditions: (1, 2, 3), (1, 2, 5), (1, 4, 5). Thus, the ABC number of T is 3.

You are given a string S. Each character of S is A, B, C or ?.

Let Q be the number of occurrences of ? in S. We can make 3^Q strings by replacing each occurrence of ? in S with A, B or C. Find the sum of the ABC numbers of all these strings.

This sum can be extremely large, so print the sum modulo 10^9 + 7.

Constraints

3 ≤ |S| ≤ 10^5

Each character of S is A, B, C or ?.

Input

Input is given from Standard Input in the following format:

S

Output

Print the sum of the ABC numbers of all the 3^Q strings, modulo 10^9 + 7.

Sample Input 1

A??C

Sample Output 1

8

In this case, Q = 2, and we can make 3^Q = 9 strings by by replacing each occurrence of ? with A, B or C. The ABC number of each of these strings is as follows:

AAAC: 0

AABC: 2

AACC: 0

ABAC: 1

ABBC: 2

ABCC: 2

ACAC: 0

ACBC: 1

ACCC: 0

The sum of these is 0 + 2 + 0 + 1 + 2 + 2 + 0 + 1 + 0 = 8, so we print 8 modulo 10^9 + 7, that is, 8.

Sample Input 2

ABCBC

Sample Output 2

3

When Q = 0, we print the ABC number of S itself, modulo 10^9 + 7. This string is the same as the one given as an example in the problem statement, and its ABC number is 3.

Sample Input 3

????C?????B??????A???????

Sample Output 3

979596887

In this case, the sum of the ABC numbers of all the 3^Q strings is 2291979612924, and we should print this number modulo 10^9 + 7, that is, 979596887.

Solution in Pascal (FPC 2.6.2) (judge verdict: Runtime Error)

var
    d,g,i,j:longint;
    f:array[0..20,0..200010] of longint;
    p,c:array[0..20] of longint;
function min(a,b:longint):longint;
begin
    if a<b then exit(a) else exit(b);
end;
function dp(n,m:longint):longint;
var
    i:longint;
begin
    if m<=0 then exit(0);
    if n=0 then exit(999999999);
    if f[n,m]<>999999999 then exit(f[n,m]);
    for i:=0 to p[n]-1 do
        f[n,m]:=min(f[n,m],dp(n-1,m-i*n)+i);
    f[n,m]:=min(f[n,m],dp(n-1,m-p[n]*n-c[n])+p[n]);
    exit(f[n,m]);
end;
begin
    readln(d,g);g:=g div 100;
    for i:=1 to d do
        begin
            readln(p[i],c[i]);
            c[i]:=c[i] div 100;
        end;
    for i:=1 to d do
        for j:=1 to g do
            f[i,j]:=999999999;
    writeln(dp(d,g));
end.