Insecure PRNG

Using a PRNG that isn't proven to be cryptographically secure is a recipe for disaster

Discuss The Problem

After inspecting the source code, you've learned that an online bitcoin wallet generator is using a linear congruential generator as a source of randomness to generate bitcoin secret keys.
The parameters being used are from glibc's LCG implementation
$m = 2^{31}$
$a = 1103515245$
$c = 12345$

The only difference being a very slight security upgrade, in which each iteration only outputs one bit, N >> 29 & 1. When generating a new secret key 256 iterations are used to generate 256 "random" bits, which are used as the secret key. You requested a new random private key and the server gave you this (in Wallet Import Format):

What will be the next secret key generated? (submit the solution in WIF)

Test Vector

If the specified LCG is initiated with the seed $0x123$, the first 256 bits of output is:
Which when converted to WIF is: