CF932G.Palindrome Partition

Given a string $s$ , find the number of ways to split $s$ to substrings such that if there are $k$ substrings $(p_{1},p_{2},p_{3},...,p_{k})$ in partition, then $p_{i}=p_{k-i+1}$ for all $i$ $(1<=i<=k)$ and $k$ is even.

Since the number of ways can be large, print it modulo $10^{9}+7$ .

The only line of input contains a string $s$ $(2<=|s|<=10^{6})$ of even length consisting of lowercase Latin letters.

Print one integer, the number of ways of partitioning the string modulo $10^{9}+7$ .

In the first case, the only way to partition the string is $ab|cd|cd|ab$ .

In the second case, the string can be partitioned as $ab|b|ab|ab|ab|ab|b|ab$ or $ab|b|abab|abab|b|ab$ or $abbab|ab|ab|abbab$ .