Array Concatanation

Count the number of boolean arrays with $a$ zeroes and $b$ ones, such that the following holds. Let $A$ be the boolean array and $A_i$ = $\text{subarray}$($A_1$, $A_2$ .... $A_i$). Concatenate $A_1$, $A_2$ ... $A_{a+b}$ and call this array $B$. The number of ones on odd and even indexes in the array $B$ are equal. Print the answer modulo $1000000007$. **Note: $a$ + $b$ is always even.** ### I