AksLolCoding has an integer (x) and a list of (n) operations. Each operation is a string starting with one of the symbols +,-,x, or / (representing addition, subtraction, multiplication, and real number division respectively), followed immediately by a positive integer (y) ((1 \leq y \leq 10^9)). For example, the operation x3 represents multiplying (x) by (3). AksLolCoding will randomly permute the operations and then apply all operations sequentially to (x) in the permuted order. Help AksLolCoding compute the expected(^{\text{∗}}) final value of (x) modulo (10^9+7). Formally, let (M = 10^9 + 7). It can be shown that the answer can be expressed as an irreducible fraction (\frac{p}{q}), where (p) and (q) are integers and (q \not\equiv 0 \pmod M). Output the integer equal to (p \cdot q^{-1} \pmod M). In other words, output such an integer (a) that (0 \le a \lt M) and (a \cdot q \equiv p \pmod M). (^{\text{∗}})The expected final value of (x) is the average of the final value of (x) over all (n!) permutations. The first line contains a single integer (t) ((1 \leq t \leq 1000)), the number of test cases. For each test case, the first line contains two integers (n) and (x) ((1 \leq n \leq 3000), (1 \leq x \leq 10^9)). The second line of each test case contains (n) strings, each representing an operation in the format described above. The sum of (n^2) over all test cases does not exceed (3000^2). Note: x is used to represent multiplication, not * For each test case, output a single integer: the expected final value of (x) modulo (10^9+7). In the first test case, (x) can either be ((10\cdot 2)-10=10) or ((10-10)\cdot 2=0), resulting in an expected value of (5). In the second test case, all possible permutations result in (x=2). In the third test case, the expected value of (x) is (\frac{55}{6}).