l.cpp

#include <bits/stdc++.h>

typedef int64_t Int;

const Int mod = (Int)1e9+7;

// Sum of arithmetic progression: 1 + 2 + ... + last = last * (last+1) / 2
Int sum(Int last) {
    return last * (last+1) % mod * ((mod+1) / 2) % mod;
}

// Calculate sum of walks between each pair of vertices in caterpillar tree:
Int solve(const std::vector<Int> & d) {
    Int answer = 0, n = (Int)d.size();

    // Calculate sum of walks between each pair of main vertices:
    for (Int last = n-1; last > 0; --last) {
        answer = (answer + sum(last)) % mod;
    }

    // Calculate sum of walks between each pair from main and additional vertices:
    for (Int i = 0; i < n; ++i) {
        answer = (answer + sum(i+1) * d[i] % mod) % mod;
        answer = (answer + sum(n-i) * d[i] % mod) % mod;
    }
    answer = (answer + mod - std::accumulate(d.begin(), d.end(), Int(0))) % mod; // substract repetitive walks

    // Calculate sum of walks between each pair of additional vertices in one group:
    for (Int i = 0; i < n; ++i) {
        answer = (answer + d[i] * (d[i]-1) % mod) % mod;
    }

    // Calculate suffix sums over vector d:
    // suffix1[i] = d[i] + d[i+1] + d[i+2] + ... + d[n-1]
    // suffix2[i] = (i+1) * d[i] + (i+2) * d[i+1] + (i+3) * d[i+2] + ... + n * d[n-1]
    std::vector<Int> suffix1(n+1, 0), suffix2(n+1, 0);
    for (Int i = n-1; i >= 0; --i) {
        suffix1[i] = (suffix1[i+1] + d[i]) % mod;
        suffix2[i] = (suffix2[i+1] + d[i] * (i+1)) % mod;
    }

    // Calculate walks between each pair of vertices from different groups:
    for (Int i = 0; i < n; ++i) {
        Int mul = (suffix2[i+1] + (mod + 1 - i) * suffix1[i+1] % mod) % mod;
        answer = (answer + d[i] * mul % mod) % mod;
    }

    return answer;
}

int main() {
    std::ios_base::sync_with_stdio(false); std::cin.tie(0); std::cout.tie(0);

    Int n; std::cin >> n;

    std::vector<Int> d(n); for (auto& it : d) std::cin >> it;

    std::cout << solve(d) << std::endl;

    return 0;
}