Valid Assignments

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"### Problem Given an array $B$ of $N$ integer elements and an integer $X$. We have to assign value to elements of an array $A$ of size $N + 1$. It is given that $A[0] = X$. Array $B$ follows the given property: - $B[0] = 0$. - $B[i] = 1$. We have to assign value to each array element in array $A$ for $1 \leq i \leq N$ such that: - The maximum possible value assigned is $X$. - The value assigned to any array element must be positive. - The value assigned to the element at index $i$ is less than or equal to the value assigned to the element at index $B[i]$, i.e., $A[i] \leq A[B[i]]$. Find the number of valid assignments possible modulo $10^9 + 7$. It is guaranteed that the value of array $B$ is such that there does not exist any pair of indices $(i,j)$ in array $A$ such that both conditions hold simultaneously: - Value assigned to element at index $i$ i.e. $A[i]$ is less than or equal to value assigned to element at index $j$ i.e. $A[j]$. - Value assigned to element at index $j$ i.e. $A[j]$ is less than or equal to value assigned to element at index $i$ i.e. $A[i]$. ### Input - $T$: Number of test cases - $N$: Size of array $B$ - $X$: Maximum possible value - $B$: Array $B$ of $N$ integer elements ### Output - The number of valid assignments possible modulo $10^9 + 7$"