Static range queries

// 1-based indexing is often easier
for (int i = 1; i <= n; i++) {
    pref[i] = pref[i-1] + a[i];
}

// Sum of range [L, R]
long long sum = pref[R] - pref[L-1];

for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
        pref[i][j] = a[i][j] + pref[i-1][j] + pref[i][j-1] - pref[i-1][j-1];
    }
}

// Query
long long sum = pref[x2][y2] - pref[x1-1][y2] - pref[x2][y1-1] + pref[x1-1][y1-1];

diff[L] += V;
diff[R+1] -= V;

// Recover original array
for (int i = 1; i <= n; i++) {
    val[i] = val[i-1] + diff[i];
}