multitestcase

math/factorial/gen/example_00.in

@@ -1 +1,6 @@
+5
 0
+5
+100
+1234567
+998244352

math/factorial/gen/near_half.cpp

@@ -6,7 +6,11 @@ int main(int, char* argv[]) {
   long long seed = atoll(argv[1]);
   auto gen = Random(seed);
 
-  int N = gen.uniform<int>(0.45 * MOD, 0.55 * MOD);
-  printf("%d\n", N);
+  int T = T_MAX;
+  printf("%d\n", T);
+  for (int t = 0; t < T; ++t) {
+    int N = gen.uniform<int>(0.45 * MOD, 0.55 * MOD);
+    printf("%d\n", N);
+  }
   return 0;
 }

math/factorial/gen/near_max.cpp

@@ -6,7 +6,11 @@ int main(int, char* argv[]) {
   long long seed = atoll(argv[1]);
   auto gen = Random(seed);
 
-  int N = gen.uniform<int>(0.95 * MOD, MOD - 1);
-  printf("%d\n", N);
+  int T = T_MAX;
+  printf("%d\n", T);
+  for (int t = 0; t < T; ++t) {
+    int N = gen.uniform<int>(0.95 * MOD, MOD - 1);
+    printf("%d\n", N);
+  }
   return 0;
 }

math/factorial/gen/random.cpp

@@ -6,7 +6,11 @@ int main(int, char* argv[]) {
   long long seed = atoll(argv[1]);
   auto gen = Random(seed);
 
-  int N = gen.uniform<int>(0, MOD - 1);
-  printf("%d\n", N);
+  int T = T_MAX;
+  printf("%d\n", T);
+  for (int t = 0; t < T; ++t) {
+    int N = gen.uniform<int>(0, MOD - 1);
+    printf("%d\n", N);
+  }
   return 0;
 }

math/factorial/hash.json

@@ -1,36 +1,16 @@
 {
-  "example_00.in": "9a271f2a916b0b6ee6cecb2426f0b3206ef074578be55d9bc94f6f3fe3ab86aa",
-  "example_00.out": "6b86b273ff34fce19d6b804eff5a3f5747ada4eaa22f1d49c01e52ddb7875b4b",
-  "example_01.in": "eea8254c7500ba3de996aa8ad6af399183f04e17d4a8102fde539dbc93a90012",
-  "example_01.out": "54a9294060a94f5166e0902704b34c0ddf9e913148e80e2224213ff4c6665a99",
-  "example_02.in": "d94b5d5e2010ceb1f753093c4b1111b0c411837daf56c8415056eb92346a0bcd",
-  "example_02.out": "0b274a87936f26e505c159427061edb5d54cc742f78ed7cf8c5e8c58c08639f8",
-  "near_half_00.in": "4d20fea3b1b8f1331ca5c417cc2fe9829dad91921dd6783810b1d2f1ad97db6a",
-  "near_half_00.out": "db0a34160e386d1388ad3c24a46a2ca0be698e4b3754a88dff16b691f92bf35a",
-  "near_half_01.in": "5936077669c4ed43c2b811b52586d429b2423f75476729a676770a51cc9bb961",
-  "near_half_01.out": "7179dadb7caea3c1461a9bcc5ba46e0533273bd1467b0b7589c5b6a510912689",
-  "near_half_02.in": "db21c9ce914ed36e55404989c0b918c43745f23bac2ac17fd756c74a8807b68c",
-  "near_half_02.out": "a85975397f8ac5d98d0bf1c7dfd17a8d37bfa039eb7642ec36ec319a347da5b8",
-  "near_max_00.in": "ca42e336242d5cdee76c8cf0213094783658996772d25f0859d100dbd33e302f",
-  "near_max_00.out": "963161328cf7fc7937e5e8830bffff9cfb68ba5ed8c4deb3e180c1488e17910c",
-  "near_max_01.in": "9d9d4a87eef24902715b2518acdafb773c3096eb6a26bfbc4229d16165f9ffc3",
-  "near_max_01.out": "c859d0646c408f6dfebcced73cc962f1545ebd049faa4182ef2bb41832b5e287",
-  "near_max_02.in": "ab0c9e20428c77ee2fe37ba96bce43e9d10cfcece467626d4aae3de35c4b80bf",
-  "near_max_02.out": "9baf06b85dafe7a017d412e554b2fdad3def30ba119c78f862bb1363b7f8a23c",
-  "random_00.in": "3cfdf017bf8e88510a8d2d670a5736b66267d2e4af13d68a60871013426e0a01",
-  "random_00.out": "5e22b5482b97861082f608ae4937af5aeaade883e71e7b8e15f237e73a4fd86c",
-  "random_01.in": "7e6d42e3a77c2d80f2a05fd9e601e1c1a15271717eb454400e510b5ec92ca4fe",
-  "random_01.out": "81000415cae1b568ce2d3203dc1e68eccd3ce601af791f9eb12b86fcf66c4233",
-  "random_02.in": "751ae5dea0048ddcce5248cf2334982830420a40ff5cba50790018073d65ebc5",
-  "random_02.out": "c03fee4d693dba8cb8dd66baf974e5d3c8975dbca7ce2567c048f9642c2e057b",
-  "random_03.in": "af3f76179322d5f9409d5fc655ae7f5e6ec6a572a0df43e580f552cbea13a9f2",
-  "random_03.out": "9b4a83229a0593fa3febf4943ebff8e89304a7b9e05385e404a35a4e91752c38",
-  "random_04.in": "2581a6e5ce00ad8fc8de99c4e6bec594642a729e4668f306e7047b4f29b2cab7",
-  "random_04.out": "8692bc2cf1ca11b2db337f4077f642e5cdcc44042b1b1899b850c038178b2220",
-  "random_05.in": "48d53f8ced4a76f9e8a5256816877a715aee9e3c8b75e2ca09789477f129983e",
-  "random_05.out": "c7730e9c08817d489536d442d3a344405f09c9b63562479241d90485ecb04f01",
-  "random_06.in": "da95bcd27b9626ef0cda5fd78625b1706e1927f5530f3e138210effcd8a9975b",
-  "random_06.out": "1315fc99f118eba7116dc7ff4c13515d76859c49438b0f834d2a3767dc4e5411",
-  "random_07.in": "bcb2ae24fafc8c1c714cb98c83df708cade5c68b3a40919da635ef1f4139560e",
-  "random_07.out": "045b1dd57d704ccc139564afe0467f6f0335d22214a2585124e8c2e6379dcdc4"
+  "example_00.in": "180d1bbdde5539dd3a77d325f8940297325665f9f1be249c051dad6aa177200a",
+  "example_00.out": "c73d2af1573bc3649136764834711acaf148eb3588cc639d8bf5a57da9bdd867",
+  "near_half_00.in": "b9b509e96007f2595f9a1845c56544b107a20794261c0a3913056ebc1c472d48",
+  "near_half_00.out": "09c498ab37ca56ec5d94ca104802a0a8fbc78539941f994880463e874cb5e266",
+  "near_half_01.in": "78c59f15afe18136e693628e08aa54d462218ac825d29667c75f5d0e6044babc",
+  "near_half_01.out": "0d58b0459853ec01a08a006ee4f2288c2304264e5551b3a0d65b93dfe111620b",
+  "near_max_00.in": "da530850d58cc2e3e79f6104dc0af91b76a0ec7d61fc5120b4487f2a94312d6f",
+  "near_max_00.out": "06f27a007c8c14ad2cb868844bd5a5e94346dc144ee51b6446a1b684a104902f",
+  "near_max_01.in": "2d4f31d5ddec6a701ed69d204aaa8c49439066f4d675fd99774795757358dc3c",
+  "near_max_01.out": "3655b1fb1215b40a9c762042096ef89af95e7aa94da5ca63b7daf72263c023a1",
+  "random_00.in": "ef2dc732889096480a438e542b5dc79018083e8771651ef8ffa37b0fd1f6c246",
+  "random_00.out": "65ac0924d4ca6ff146997bc802a42aec719d48cc8556127fc2f5d514efaef047",
+  "random_01.in": "0842027f68881d70d3376224a68b92f9e19f13840ef9d573acdba3c85d1fc1d0",
+  "random_01.out": "bd08bbc7d8dd2d279da20ce0ba42d99198728e7b3faccc03ab24c4d5576066f1"
 }

math/factorial/info.toml

@@ -1,24 +1,25 @@
 title = 'Factorial'
-timelimit = 5.0
+timelimit = 10.0
 forum = "https://github.com/yosupo06/library-checker-problems/issues/128"
 
 [[tests]]
     name = "example.in"
-    number = 3
+    number = 1
 [[tests]]
     name = "random.cpp"
-    number = 8
+    number = 2
 [[tests]]
     name = "near_max.cpp"
-    number = 3
+    number = 2
 [[tests]]
     name = "near_half.cpp"
-    number = 3
+    number = 2
 
 [[solutions]]
     name = "naive.cpp"
     wrong = false
 
 
 [params]
+    T_MAX = 5
     MOD = 998244353

math/factorial/sol/correct.cpp

@@ -635,10 +635,12 @@ void solve() {
   scanf("%d", &N);
   vc<mint> f = {1, 1};
   mint b = prefix_product_of_poly(f, N);
-  printf("%d", b.val);
+  printf("%d\n", b.val);
 }
 
 signed main() {
-  solve();
+  int T;
+  scanf("%d", &T);
+  for (int t = 0; t < T; ++t) solve();
   return 0;
 }

math/factorial/sol/naive.cpp

@@ -7,13 +7,29 @@ constexpr int mod = 998244353;
 void solve() {
   int N;
   scanf("%d", &N);
-
-  long long ans = 1;
-  for (int n = 1; n <= N; ++n) ans = ans * n % mod;
-  printf("%lld", ans);
+  if (N < mod / 2) {
+    long long x = 1;
+    for (int n = 1; n <= N; ++n) x = x * n % mod;
+    printf("%lld\n", x);
+  } else {
+    long long x = mod - 1; // (mod-1)!
+    long long y = 1;
+    for (int n = N + 1; n <= mod - 1; ++n) { y = y * n % mod; }
+    // x / y
+    // xy^{mod-2}
+    long long n = mod - 2;
+    while (n) {
+      if (n & 1) x = x * y % mod;
+      y = y * y % mod;
+      n /= 2;
+    }
+    printf("%lld\n", x);
+  }
 }
 
 signed main() {
-  solve();
+  int T;
+  scanf("%d", &T);
+  for (int t = 0; t < T; ++t) solve();
   return 0;
 }

math/factorial/task.md

@@ -2,37 +2,40 @@
 
 @{lang.en}
 
+This problem has $T$ cases.
+
 Given a non-negative integer $N$. Print $N!$ modulo $@{param.MOD}$. 
 
 @{lang.ja}
 
+この問題は $T$ ケースあります．
 非負整数 $N$ が与えられます．$N!$ を $@{param.MOD}$ で割った余りを出力してください．
 
 @{lang.end}
 
 ## @{keyword.constraints}
 
+- $1\leq T\leq 5$
 - $0 \leq N < @{param.MOD}$
 
 ## @{keyword.input}
 
 ```
-$N$
+$T$
+$N_1$
+$\vdots$
+$N_T$
 ```
 
 ## @{keyword.output}
 @{lang.en}
-Given a non-negative integer $N$. Print $N!$ modulo $@{param.MOD}$. 
+Print $N!$ modulo $@{param.MOD}$. 
 
 @{lang.ja}
 
-非負整数 $N$ が与えられます．$N!$ を $@{param.MOD}$ で割った余りを出力してください．
+$N!$ を $@{param.MOD}$ で割った余りを出力してください．
 @{lang.end}
 
 ## @{keyword.sample}
 
 @{example.example_00}
-
-@{example.example_01}
-
-@{example.example_02}

math/factorial/verifier.cpp

@@ -4,8 +4,12 @@
 
 int main() {
   registerValidation();
-  inf.readLong(0, MOD - 1);
+  int T = inf.readInt(1, T_MAX);
   inf.readChar('\n');
+  for (int t = 0; t < T; ++t) {
+    inf.readLong(0, MOD - 1);
+    inf.readChar('\n');
+  }
   inf.readEof();
   return 0;
 }