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| #include <algorithm>
#include <bits/stdc++.h>
#include <cstdio>
#ifndef LOCAL
#define debug(...)
#else
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#endif
#define rep1(a) for (int i = 0; i < a; i++)
#define rep2(i, a) for (int i = 0; i < a; i++)
#define rep3(i, a, b) for (int i = a; i < b; i++)
#define rep4(i, a, b, c) for (int i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define pb emplace_back
using namespace std;
template <typename T, typename T2> void cmin(T &x, const T2 &y) {
x = x < y ? x : y;
}
template <typename T, typename T2> void cmax(T &x, const T2 &y) {
x = x > y ? x : y;
}
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
template <class T> using vc = vector<T>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
mt19937 rng(time(NULL));
const int inf = 1000000000;
const ll lnf = 1000000000000000000;
#define sz(x) int((x).size())
#define all(x) begin(x), end(x)
template <class... T> void read() {}
template <class T> void read(T &x) { cin >> x; }
template <class T, class S> void read(pair<T, S> &v) {
read(v.first, v.second);
}
template <class T> void read(vector<T> &v) {
for (T &x : v)
read(x);
}
template <class T, class... Ts> void read(T &a, Ts &...b) {
read(a), read(b...);
}
void solve() {
int n, c;
cin >> n >> c;
vi dif(n);
string s;
cin >> s;
int cnt = 0;
rep(i, n) {
if (s[i] == s[n - 1 - i]) dif[i] = 0;
else dif[i] = 1, cnt++;
}
cnt /= 2;
vi h(n);
read(h);
vi p(n);
ll t = 0;
int w = 0;
int L = 1, R = 0;
auto add = [&](int x) {
if (!dif[x]) {
return;
}
int y = min(x, n - 1 - x);
p[y] += 1;
if (p[y] == 1) {
t += h[x];
w += 1;
} else {
t -= h[n - 1 - x];
t += min(h[x], h[n - 1 - x]);
}
};
auto del = [&](int x) {
if (!dif[x]) {
return;
}
int y = min(x, n - 1 - x);
p[y] -= 1;
if (p[y] == 0) {
t -= h[x];
w -= 1;
} else {
t -= min(h[x], h[n - 1 - x]);
t += h[n - 1 - x];
}
};
auto calc = [&](int l, int r) {
while (L > l) {
add(--L);
}
while (R < r) {
add(++R);
}
while (L < l) {
del(L++);
}
while (R > r) {
del(R--);
}
};
vc<ll> ans(n, lnf);
auto solve = [&](auto self, int l, int r, int a, int b) -> void {
if (l > r) {
return;
}
debug(l, r, a, b);
int m = (l + r) / 2;
int p = max(m, a);
calc(m, p);
while (p + 1 < n && w < cnt) {
p += 1;
calc(m, p);
}
if (w < cnt) {
self(self, l, m - 1, a, p);
return;
}
ll res = t + 1ll * (p - m) * c;
for (int i = p; i <= b; i++) {
calc(m, i);
if (res > t + 1ll * (i - m) * c) {
res = t + 1ll * (i - m) * c;
p = i;
}
}
cmin(ans[m], res);
self(self, l, m - 1, a, p);
self(self, m + 1, r, p, b);
};
t = 0, w = 0, L = 1, R = 0;
rep(i, n) p[i] = 0;
solve(solve, 0, n - 1, 0, n - 1);
reverse(all(ans));
reverse(all(h));
t = 0, w = 0, L = 1, R = 0;
rep(i, n) p[i] = 0;
solve(solve, 0, n - 1, 0, n - 1);
reverse(all(ans));
reverse(all(h));
ll mn = lnf;
for (int i = 0; i < n; i++) {
cmin(ans[i], mn + 1ll * i * c);
cmin(mn, ans[i] - 1ll * i * c);
}
reverse(all(ans));
mn = lnf;
for (int i = 0; i < n; i++) {
cmin(ans[i], mn + 1ll * i * c);
cmin(mn, ans[i] - 1ll * i * c);
}
reverse(all(ans));
for (auto x : ans) {
cout << x << " ";
}
cout << "\n";
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int t = 1;
cin >> t;
while (t--) {
solve();
}
return 0;
}
|
