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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

val MOD = 1000000000+ 7

fun main(args : Array<String>) {
    val S = readLine()!!


    val dpA = LongArray(S.length + 1)
    val dpAB = LongArray(S.length + 1)
    val dpABC = LongArray(S.length + 1)

    dpA.fill(0)
    dpAB.fill(0)
    dpABC.fill(0)

    (1..S.length).forEach {i ->
        val s = S[i - 1]
        if (s == 'A') {
            dpA[i] = (dpA[i - 1] + 1) % MOD
        } else {
            dpA[i] = dpA[i - 1] % MOD
        }

        if (s == 'B') {
            dpAB[i] = (dpAB[i - 1] + dpA[i - 1]) % MOD
        } else {
            dpAB[i] = dpAB[i - 1] % MOD
        }

        if (s == 'C') {
            dpABC[i] = (dpABC[i - 1] + dpAB[i - 1]) % MOD
        } else {
            dpABC[i] = dpABC[i - 1] % MOD
        }

        if (s == '?') {
            dpA[i] = listOf(dpA[i-1], dpA[i-1], dpA[i-1] + 1).reduce { acc, l -> add(acc,l) }
            dpAB[i] = listOf(dpAB[i-1], dpAB[i-1], dpAB[i-1] + dpA[i - 1]).reduce { acc, l -> add(acc,l) }
            dpABC[i] = listOf(dpABC[i-1], dpABC[i-1], dpABC[i-1], dpAB[i - 1]).reduce { acc, l -> add(acc,l) }
        }
    }

    println(dpABC[S.length])
}

fun add(a: Long, b: Long) : Long {
    return (a + b) % MOD
}