P1164 小A点菜

// Problem: P1164 小A点菜
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/P1164
// Memory Limit: 128 MB
// Time Limit: 1000 ms
// User: Pannnn

#include <bits/stdc++.h>

using namespace std;

template<class T>
void debugVector(const T &a) {
    cout << "[ ";
    for (size_t i = 0; i < a.size(); ++i) {
        cout << a[i] << (i == a.size() - 1 ? " " : ", ");
    }
    cout << "]" << endl;
}

template<class T>
void debugMatrix2(const T &a) {
    for (size_t i = 0; i < a.size(); ++i) {
        debugVector(a[i]);
    }
}

template<class T>
using matrix2 = vector<vector<T>>;

template<class T>
vector<vector<T>> getMatrix2(size_t n, size_t m, T init = T()) {
    return vector<vector<T>>(n, vector<T>(m, init));
}

template<class T>
using matrix3 = vector<vector<vector<T>>>;

template<class T>
vector<vector<vector<T>>> getMatrix3(size_t x, size_t y, size_t z, T init = T()) {
    return vector<vector<vector<T>>>(x, vector<vector<T>>(y, vector<T>(z, init)));
}

void printBigInteger(vector<int> a) {
    for (size_t i = a.size() - 1; i >= 0; --i) {
        cout << a[i];
    }
}
vector<int> addBigInteger(vector<int> a, vector<int> b) {
    vector<int> res;
    int pre = 0;
    for (size_t i = 0; i < a.size() || i < b.size() || pre; ++i) {
        if (i < a.size()) pre += a[i];
        if (i < b.size()) pre += b[i];
        res.push_back(pre % 10);
        pre /= 10;
    }
    return res;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    
    int n, m;
    cin >> n >> m;
    
    /*
        info[i][j]:前i道菜用光j元钱的办法总数。
        终止条件：j == 0 只有1种方案
                i == 0 && j != 0 只有0种方案
                
        每个状态在吃与不吃之间抉择，若钱充足，办法总数就是吃这道菜与不吃这道菜的办法数之和
        若不充足，办法总数就只能承袭吃前i-1道菜的办法总数。
    */
    matrix2<int> info = getMatrix2(n + 1, m + 1, 0);
    vector<int> a(n + 1);
    for (int i = 1; i <= n; ++i) {
        cin >> a[i];
    }
    for (int i = 0; i <= n; ++i) {
        info[i][0] = 1;
    }
    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j <= m; ++j) {
            if (j >= a[i]) {
                info[i][j] = info[i - 1][j] + info[i - 1][j - a[i]];
            } else {
                info[i][j] = info[i - 1][j];
            }
        }
    }
    cout << info[n][m] << endl;
    return 0;
}