n00b got into an argument with cr4wl3r.

He was using the following encryption scheme as a pseudo-random generator.

X_n+1 = a*X_n + b mod m

cr4wl3r suggested that this was a totally broken encryption scheme, but n00b is stubborn (that completely explains why he is a noob :p).

Given the following intercepts of the keys, cr4wl3r was easily able to predict the next key in the sequence and hence break the given cipher.

7038329, 2595920584582988203224023874, 7475933611109024100933403119814559969, 31747476908195446927119842689781944834, 56414337241223827095371416459206162677, 99394688082857206064008418768140322102, 109367624086937873413279568187024041009, 40725846811506101619261190275112585346, 110494169997775806409950259924752648741, 52602757756756180636420012361374566534

See if you can break it too!

ciphertext: 4cf20a8068d0f7eb60f1922ec016ef6844b44bc368cbf7e7

Hint: consider converting the next key obtained in the sequence to hex.