a.py

import numpy as np

MOD = 10 ** 9 + 7

assert ((MOD - 1) ** 2).bit_length() == 60
N = 20
assert (N * (MOD - 1) ** 2).bit_length() == 65

x = np.array([MOD - 1] * N, dtype=np.int64)
assert x.dot(x) % MOD == 417656019  # incorrect answer

upper = x // (2 ** 15)
lower = x % (2 ** 15)
r30 = (2 ** 30) % MOD
r15 = (2 ** 15) % MOD
ret = (
    lower.dot(lower) % MOD +  # max: N * 2 ** 30
    lower.dot(upper) * 2 * r15 % MOD +  # max: N * 2 ** 46
    upper.dot(upper) * r30 % MOD  # max: N * 2 ** 57, safe??
) % MOD
assert ret == N  # correct answer