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vector<ll> add, mul;
void update(int l, int r, ll val) {
for (int tl = l + 1; tl < sz(add); tl += tl&(-tl))
add[tl] += val, mul[tl] -= val * l;
for (int tr = r + 1; tr < sz(add); tr += tr&(-tr))
add[tr] -= val, mul[tr] += val * r;
}
void init(vector<ll>& v) {
mul.assign(sz(v) + 1,0);
add.assign(sz(v) + 1,0);
for(int i = 0; i < sz(v); i++) update(i, i + 1, v[i]);
}
ll prefix_sum (int i) {
ll res = 0;
for (int ti = i; ti > 0; ti -= ti&(-ti))
res += add[ti] * i + mul[ti];
return res;
}
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