def test_crt_bound():
inf = NUMERIC_MAX_LL
pred = []
for i in range(1, 11):
pred.append(i)
pred.append(inf - (i - 1))
pred.append(998244353)
pred.append(1_000_000_007)
pred.append(1_000_000_009)
for ab in [[inf, inf], [1, inf], [inf, 1], [7, inf], [inf // 337, 337],
[2, (inf - 1) // 2]]:
a, b = ab
for ph in range(2):
for ans in pred:
res = crt([ans % a, ans % b], [a, b])
lcm = a // gcd(a, b) * b
assert lcm == res[1]
assert ans % lcm == res[0]
a, b = b, a
factor_inf = [49, 73, 127, 337, 92737, 649657]
for p in itertools.permutations(factor_inf):
p = list(p)
for ans in pred:
r = []
m = []
for f in p:
r.append(ans % f)
m.append(f)
res = crt(r, m)
assert ans % inf == res[0]
assert inf == res[1]
factor_infn1 = [2, 3, 715827883, 2147483647]
for p in itertools.permutations(factor_infn1):
p = list(p)
for ans in pred:
r = []
m = []
for f in p:
r.append(ans % f)
m.append(f)
res = crt(r, m)
assert ans % (inf - 1) == res[0]
assert inf - 1 == res[1]
def test_crt_overflow():
r0 = 0
r1 = 10**12 - 2
m0 = 900577
m1 = 10**12
res = crt([r0, r1], [m0, m1])
assert m0 * m1 == res[1]
assert r0 == res[0] % m0
assert r1 == res[0] % m1
def test_crt2():
for a in range(1, 21):
for b in range(1, 21):
for c in range(-10, 11):
for d in range(-10, 11):
res = crt([c, d], [a, b])
if res[1] == 0:
for x in range(a * b // gcd(a, b)):
assert x % a != c or x % b != d
continue
assert a * b // gcd(a, b) == res[1]
assert c % a == res[0] % a
assert d % b == res[0] % b
def test_crt3():
for a in range(1, 6):
for b in range(1, 6):
for c in range(1, 6):
for d in range(-5, 6):
for e in range(-5, 6):
for f in range(-5, 6):
res = crt([d, e, f], [a, b, c])
lcm = a * b // gcd(a, b)
lcm = lcm * c // gcd(lcm, c)
if res[1] == 0:
for x in range(lcm):
assert (x % a != d or x % b != e
or x % c != f)
continue
assert lcm == res[1]
assert d % a == res[0] % a
assert e % b == res[0] % b
assert f % c == res[0] % c
def test_crt_hand():
res = crt([1, 2, 1], [2, 3, 2])
assert res[0] == 5
assert res[1] == 6