def attack(p, s, s_, x, y, xs):
"""
Forges a share to recombine into a new shared secret, s', if a single share and the x coordinates of the other participants are given.
:param p: the prime used for Shamir's secret sharing
:param s: the original shared secret
:param s_: the target shared secret, s'
:param x: the x coordinate of the given share
:param y: the y coordinate of the given share
:param xs: the x coordinates of the other participants (excluding the x coordinate of the given share)
:return: the forged share
"""
const = 1
for i in xs:
const *= i * pow(i - x, -1, p)
return ((s_ - s) * pow(const, -1, p) + y) % p
