init

9C.py

@@ -0,0 +1,91 @@
+import sys
+
+input_data = sys.stdin.read().split()
+if not input_data:
+    sys.exit()
+
+MOD = 998244353
+G = 3
+
+def ntt(a, invert):
+    n = len(a)
+    j = 0
+    for i in range(1, n):
+        bit = n >> 1
+        while j & bit:
+            j ^= bit
+            bit >>= 1
+        j ^= bit
+        if i < j:
+            a[i], a[j] = a[j], a[i]
+    step = 2
+    while step <= n:
+        half = step >> 1
+        wlen = pow(G, (MOD - 1) // step, MOD)
+        if invert:
+            wlen = pow(wlen, MOD - 2, MOD)
+        w = [1] * half
+        curr = 1
+        for i in range(half):
+            w[i] = curr
+            curr = (curr * wlen) % MOD
+        for i in range(0, n, step):
+            for j in range(half):
+                u = a[i + j]
+                v = (a[i + j + half] * w[j]) % MOD
+                a[i + j] = (u + v) % MOD
+                a[i + j + half] = (u - v + MOD) % MOD
+        step <<= 1
+    if invert:
+        n_inv = pow(n, MOD - 2, MOD)
+        for i in range(n):
+            a[i] = (a[i] * n_inv) % MOD
+
+def multiply(a, b):
+    if not a or not b:
+        return []
+    sz = len(a) + len(b) - 1
+    n = 1
+    while n < sz:
+        n <<= 1
+    a = a + [0] * (n - len(a))
+    b = b + [0] * (n - len(b))
+    ntt(a, False)
+    ntt(b, False)
+    for i in range(n):
+        a[i] = (a[i] * b[i]) % MOD
+    ntt(a, True)
+    return a[:sz]
+t = int(input_data[0])
+ptr = 1
+for _ in range(t):
+    if ptr >= len(input_data):
+        break
+    n = int(input_data[ptr])
+    s = input_data[ptr+1]
+    ptr += 2
+    A = [0] * n
+    B = [0] * n
+    for i in range(n):
+        if s[i] == 'V':
+            A[i] = 1
+        elif s[i] == 'K':
+            B[n - 1 - i] = 1
+    C = multiply(A, B)
+    bad = [False] * (n + 1)
+    for k in range(len(C)):
+        if C[k] > 0:
+            dist = abs(n - 1 - k)
+            if dist <= n:
+                bad[dist] = True    
+    ans = []
+    for p in range(1, n + 1):
+        valid = True
+        for m in range(p, n + 1, p):
+            if bad[m]:
+                valid = False
+                break
+        if valid:
+            ans.append(p)            
+    print(len(ans))
+    print(*(ans))