Multiplying Large Polynomials

We define the functions $\mathrm{polyRep}$ and $\mathrm{strRep}$ in the context for polynomials with coefficients from $GF(2)$ as follows:

$\mathrm{strRep}(\sum_{i=0}^{n-1}a_ix^i) = \overline{a_0a_1 \cdots a_{n-1}} \\ \mathrm{polyRep}(\overline{a_0a_1 \cdots a_{n-1}}) = \sum_{i=0}^{n-1}a_ix^i$

Given two $n$ -bit strings $A$ and $B$ , and another $n+1$ bit string $P$ , we define their $P$ product as

$\mathrm{Prod}_P{(A, B)} = \mathrm{strRep}\left (c \times \mathrm{polyRep}(B) \pmod{\mathrm{polyRep}(P)}\right )$

where the multiplication is considered as multiplication of polynomials over $GF(2)$ .

A natural definition of exponentiation is immediate:

$\mathrm{Exp}_P(A,k) = \mathrm{strRep} \left ( \mathrm{polyRep}(A^k) \pmod{ \mathrm{polyRep}(k)} \right )$

Compute $\mathrm{Exp}_P(A,k)$ for the given values and let $r$ be the result. Enter your answer as the number of 1s in $r$ .

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P = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000001
A = 0000100011010110011100111011001001001101000100100011111011110001010001000101111101101010000100110010
k = 2017

This problem is taken from a list of problems posted by RC Bose Center of Cryptography.