#include <bits/stdc++.h>
#include <sstream>
using namespace std;

typedef long long LL;

const int N = 120;
const int MOD = 1e9 + 7;

struct exps
{
    vector<string> a[N]; // x^i的系数
    int i; // 最高次幂
};

vector<string> eq;
stack<exps> eq2;
unordered_map<string, int> f;
int val[N];
int n, m;

void get_idx(string x)
{
    if (f[x]) return;
    int idx = 0;
    for (int i = 1; i < x.size(); i++)
        idx = idx * 10 + x[i] - '0';
    f[x] = idx;
}

void _proc(string op, int x)
{
    exps x1, x2, nx;
    x2 = eq2.top(); eq2.pop();
    x1 = eq2.top(); eq2.pop();

    if (op == "+" || op == "-")
    {
        nx.i = max(x1.i, x2.i);
        for (int i = 0; i <= max(x1.i, x2.i); i++)
        {
            if (!x1.a[i].size() && !x2.a[i].size()) continue;
            nx.a[i] = x1.a[i];
            if (!x1.a[i].size()) nx.a[i].push_back("0");
            nx.a[i].insert(nx.a[i].end(), x2.a[i].begin(), x2.a[i].end());
            if (x2.a[i].size()) nx.a[i].push_back(op);
        }
    }

    else // 乘法
    {
        nx.i = x1.i + x2.i;
        for (int i = 0; i <= x1.i; i++)
        {
            for (int j = 0; j <= x2.i; j++)
            {
                bool flag = false;
                if (nx.a[i + j].size()) flag = true;
                if (x1.a[i].size() && x2.a[j].size())
                {
                    nx.a[i + j].insert(nx.a[i + j].end(), x1.a[i].begin(), x1.a[i].end());
                    nx.a[i + j].insert(nx.a[i + j].end(), x2.a[j].begin(), x2.a[j].end());
                    nx.a[i + j].push_back(op);
                    if (flag) nx.a[i + j].push_back("+");
                }
            }
        }
    }

    eq2.push(nx);
}

void proc(int x)
{
    for (auto t : eq)
    {
        if (t == "+" || t == "-" || t == "*") _proc(t, x);
        else
        {
            if (f[t] == x) 
            {
                exps e;
                e.a[1] = {"1"};
                e.i = 1;
                eq2.push(e);
            }
            else
            {
                exps e;
                e.a[0] = {t};
                e.i = 0;
                eq2.push(e);
            }
        } 
    }
}

LL str2num(string s)
{
    bool isneg = false;
    int i = 0;
    if (s[0] == '-') 
    {
        isneg = true;
        i++;
    }

    LL res = 0;
    for (; i < s.size(); i++)
    {
        res = res * 10 + s[i] - '0';
    }

    if (isneg) res = -res;
    return res;
}

LL get_val(vector<string> e)
{
    stack<LL> stk;
    for (auto t : e)
    {
        if (t == "+" || t == "-" || t == "*")
        {
            LL x2 = stk.top(); stk.pop();
            LL x1 = stk.top(); stk.pop();
            LL res;

            if (t == "+") res = (x1 + x2) % MOD;
            else if (t == "-") res = (x1 - x2) % MOD;
            else res = x1 * x2 % MOD;
            stk.push(res);
        }

        else
        {
            if (t[0] == 'x') stk.push(val[f[t]]);
            else stk.push(str2num(t));
        }
    }

    if (stk.size() == 1) return stk.top();
    return -1;
}

LL qmi(int m, int k, int p)
{
    LL res = 1 % p, t = m;
    while (k)
    {
        if (k & 1) res = res * t % p;
        t = t * t % p;
        k >>= 1;
    }

    return res;
}

LL cal(int x)
{
    LL res = 0;
    if (eq2.size() != 1) return -1;
    else
    {
        exps e = eq2.top();
        eq2.pop();
        for (int i = 1; i <= e.i; i++)
        {
            if (e.a[i].size())
                res += i * qmi(val[x], i - 1, MOD) % MOD * get_val(e.a[i]) % MOD;
            res %= MOD;
        }
    }

    return (res + MOD) % MOD;
}

int main()
{
    scanf("%d%d", &n, &m);
    getchar();
    string line;
    getline(cin, line);
    stringstream ssin(line);
    string t;
    while (ssin >> t)
    {
        if (t[0] == 'x') get_idx(t);
        eq.push_back(t);
    }

    while (m--)
    {
        int x;
        scanf("%d", &x);
        for (int i = 1; i <= n; i++)
        {
            int v;
            scanf("%d", &v);
            val[i] = v;
        }
        proc(x);
        printf("%lld\n", cal(x));
    }

    return 0;
}

优化

按照算数表达式树的结构，递归求导