差分视角

$[l, r] \xleftarrow{+d}$
$B_i = A_i - A_{i - 1}$

$$ A_i = \sum_{j = 1}^{i} B_j \\\ \\ \\\ S_{\text{prefix}}(x) = \sum_{i = 1}^{x} A_i = \sum_{i = 1}^{x}\sum_{j = 1}^{i} B_j \\\ \\ \\\ = \sum_{i = 1}^{x}(x-i+1)B_i = (x+1)\sum_{i = 1}^{x}B_i - \sum_{i = 1}^{x}i \cdot B_i $$

$\textbf{algorithm}$
$\textbf{i) } \text{fwick[0]} \leftarrow \sum_{i = 1}^{x} B_i, \quad \text{fwick[1]} \leftarrow \sum_{i = 1}^{x} i B_i$
$\textbf{ii) change: } [l, r]$
$\quad \quad \text{fwick[0]}.add(r+1, -d), \quad \text{fwick[0]}.add(l, d)$
$\quad \quad \text{fwick[1]}.add(r+1, -(r+1)d), \quad \text{fwick[1]}.add(l, ld)$
$\textbf{ii) ask: } [l, r]$
$\quad \quad S(r) = (\text{fwick}[0].ask(r)) \times (r+1) - \text{fwick[1]}(r)$
$\quad \quad S(l -1) = (\text{fwick}[0].ask(l - 1)) \times (l) - \text{fwick[1]}(l - 1)$
$\quad \quad \textbf{ans} = S(r) - S(l - 1)$

const int maxn = 100000 + 10;
int n, m;
ll A[maxn];

// == fenwick definition ==
class Fwick {
public:
    vector<ll> C[2];
    int n;

    void resize(int n) {
        this->n = n;
        _for(i, 0, 2) C[i].resize(n + 1);
    }

    void clear() {
        _for(i, 0, 2) fill(C[i].begin(), C[i].end(), 0ll);
    }

    void add(int k, int x, ll d) {
        int i = x;
        for(; i <= n; i += lowbit(i)) C[k][i] += 1ll * d;
    }

    ll ask(int k, int x) {
        ll ans = 0;
        for(int i = x; i; i -= lowbit(i)) ans += C[k][i];
        return ans;
    }

} fwick;
// == fenwick finsihed ==

ll prefix(int x) {
    return fwick.ask(0, x) * (x + 1) - fwick.ask(1, x);
}

void init() {
    fwick.resize(maxn);
    fwick.clear();
}

int main() {
    freopen("input.txt", "r", stdin);
    scanf("%d%d", &n, &m);
    init();

    _rep(i, 1, n) {
        scanf("%lld", &A[i]);
        fwick.add(0, i, A[i] - A[i - 1]);
        fwick.add(1, i, i * (A[i] - A[i - 1]));
    }

    // then solve
    while (m--) {
        char cmd[2];
        scanf("%s", cmd);
        if(cmd[0] == 'C') {
            int l, r, d;
            scanf("%d%d%d", &l, &r, &d);

            fwick.add(0, r + 1, -1ll * d);
            fwick.add(0, l, 1ll * d);

            fwick.add(1, r + 1, -1ll * d * (r + 1));
            fwick.add(1, l, 1ll * d * l);
        }
        else {
            int l, r;
            scanf("%d%d", &l, &r);

            ll ans = prefix(r) - prefix(l - 1);
            printf("%lld\n", ans);
        }
    }
}