1 files changed, 31 insertions, 0 deletions
diff --git a/2ndary/THT/B/QG-2016/remainder.py b/2ndary/THT/B/QG-2016/remainder.py
new file mode 100755
index 0000000..6cef9df
--- /dev/null
+++ b/2ndary/THT/B/QG-2016/remainder.py
@@ -0,0 +1,31 @@
+#!/usr/bin/env python3
+TESTS = [
+    [12, 3, 8],
+    [2, 15, 17],
+    [456, 6, 1296],
+    [1234, 100, 9],
+    [11223344, 1000000, 142857],
+    [55667788, 10000000, 1000000007],
+    [1357, 24682468, 999999999],
+    [24680, 1357913579, 777777777],
+    [998, 1000000000000, 999],
+    [1234, 11111111111111, 30],
+    [1, 222222222222222, 123456789],
+    [2016, 666666666666666, 8888888888],
+    [11223344, 555666777888999, 1357924680],
+    [999999999999999967, 999999999999999877, 999999999999999989],
+    [123456789123456789, 123456789123456789, 987654321123456789]]
+
+# Gọi l là "chiều dài" của x, l = int(log10(x) + 1) hay l = len(str(x))
+# Đặt l ** 10 = a, dễ thấy y = x * (a**(n-1) + a**(n-2) + ... + a + 1)
+#                            = x * (a**n - 1) / (a - 1)
+# y chia m bằng k dư q hay x * (a**n - 1) / (a - 1) = k * m + q
+#                      <=> x * (a**n - 1) = k * (a*m - a) + q * (a - 1)
+#                      <=> q = x * (a**n - 1) % (a*m - a) / (a - 1)
+
+with open('REMAINDER.TXT', 'w') as f:
+    for x, n, m in TESTS:
+        a = 10 ** len(str(x))
+        m *= a - 1
+        p = pow(a, n, m)
+        print(x * (p - 1) % m // (a - 1), file=f)