MOD = 998244353

def main():
    import sys
    input = sys.stdin.read
    data = input().split()
    idx = 0
    N = int(data[idx])
    idx += 1
    K = int(data[idx])
    idx += 1
    A = list(map(int, data[idx:idx+N+1]))
    idx += N+1
    P = list(map(int, data[idx:idx+N]))
    idx += N
    
    parent = [0] * (N + 1)
    for j in range(1, N+1):
        parent[j] = P[j-1]
    
    depth = [0] * (N + 1)
    for j in range(1, N+1):
        depth[j] = depth[parent[j]] + 1
    
    max_depth = max(depth)
    
    inv = [1] * (max_depth + 2)
    for i in range(2, max_depth + 2):
        inv[i] = MOD - MOD // i * inv[MOD % i] % MOD
    
    C = [0] * (max_depth + 1)
    C[0] = 1
    for d in range(1, max_depth + 1):
        C[d] = C[d-1] * (K - d + 1) % MOD
        C[d] = C[d] * inv[d] % MOD
    
    ans = [0] * (N + 1)
    for j in range(N + 1):
        d = depth[j]
        current = j
        while True:
            ans[current] = (ans[current] + A[j] * C[d - depth[current]]) % MOD
            if current == 0:
                break
            current = parent[current]
    
    for i in range(N + 1):
        print(ans[i] % MOD)

if __name__ == '__main__':
    main()