1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
|
#include <bits/stdc++.h>
using namespace std;
int64_t K;
class KarySegmentTree {
private:
struct Node
{
int64_t s1;
int64_t s2;
int64_t s3;
int64_t s4;
int64_t len;
int64_t tag;
};
int64_t K;
int n;
vector<Node> tree;
int64_t add_k(int64_t a, int64_t b)
{
int64_t res = 0, p = 1;
while (a > 0 || b > 0)
{
int64_t d1 = a % K;
int64_t d2 = b % K;
res += ((d1 + d2) % K) * p;
a /= K;
b /= K;
p *= K;
}
return res;
}
int64_t mul_k(int64_t a, int64_t c)
{
c = (c % K + K) % K;
if (c == 0){
return 0;
}
int64_t res = 0, p = 1;
while (a > 0)
{
int64_t d = a % K;
res += ((d * c) % K) * p;
a /= K;
p *= K;
}
return res;
}
void pushUp(int p) {
tree[p].s1 = add_k(tree[2 * p].s1, tree[2 * p + 1].s1);
tree[p].s2 = add_k(tree[2 * p].s2, tree[2 * p + 1].s2);
tree[p].s3 = (tree[2 * p].s3 + tree[2 * p + 1].s3) % K;
tree[p].s4 = (tree[2 * p].s4 + tree[2 * p + 1].s4) % K;
}
void applyTag(int p, int64_t v) {
int64_t v0 = v % K;
int64_t vhi = v - v0;
int64_t len = tree[p].len % K;
int64_t P1 = mul_k(tree[p].s2, v0);
int64_t P2 = mul_k(vhi, tree[p].s3);
int64_t P3 = mul_k(vhi, (len * v0) % K);
tree[p].s1 = add_k(tree[p].s1, add_k(P1, add_k(P2, P3)));
tree[p].s2 = add_k(tree[p].s2, mul_k(vhi, len));
int64_t term1 = (tree[p].s3 * v0) % K;
int64_t term2 = (len * ((v0 * (v0 + 1) / 2) % K)) % K;
tree[p].s4 = (tree[p].s4 + term1 + term2) % K;
tree[p].s3 = (tree[p].s3 + len * v0) % K;
tree[p].tag = add_k(tree[p].tag, v);
}
void pushDown(int p) {
if (tree[p].tag != 0)
{
applyTag(2 * p, tree[p].tag);
applyTag(2 * p + 1, tree[p].tag);
tree[p].tag = 0;
}
}
void build(int p, int l, int r, const vector<int64_t> &arr)
{
tree[p].len = r - l + 1;
tree[p].tag = 0;
if (l == r)
{
int64_t a0 = arr[l] % K;
int64_t ahi = arr[l] - a0;
tree[p].s1 = mul_k(ahi, a0);
tree[p].s2 = ahi;
tree[p].s3 = a0;
tree[p].s4 = (a0 * (a0 + 1) / 2) % K;
return;
}
int mid = l + (r - l) / 2;
build(2 * p, l, mid, arr);
build(2 * p + 1, mid + 1, r, arr);
pushUp(p);
}
void updateInternal(int p, int l, int r, int ql, int qr, int64_t v)
{
if (ql <= l && r <= qr)
{
applyTag(p, v);
return;
}
pushDown(p);
int mid = l + (r - l) / 2;
if (ql <= mid){
updateInternal(2 * p, l, mid, ql, qr, v);
}
if (qr > mid){
updateInternal(2 * p + 1, mid + 1, r, ql, qr, v);
}
pushUp(p);
}
Node queryInternal(int p, int l, int r, int ql, int qr)
{
if (ql <= l && r <= qr){
return tree[p];
}
pushDown(p);
int mid = l + (r - l) / 2;
if (qr <= mid){
return queryInternal(2 * p, l, mid, ql, qr);
}
if (ql > mid){
return queryInternal(2 * p + 1, mid + 1, r, ql, qr);
}
Node leftNode = queryInternal(2 * p, l, mid, ql, qr);
Node rightNode = queryInternal(2 * p + 1, mid + 1, r, ql, qr);
Node res;
res.s1 = add_k(leftNode.s1, rightNode.s1);
res.s2 = add_k(leftNode.s2, rightNode.s2);
res.s3 = (leftNode.s3 + rightNode.s3) % K;
res.s4 = (leftNode.s4 + rightNode.s4) % K;
return res;
}
public:
KarySegmentTree(int size, int64_t k_val, const vector<int64_t> &arr)
{
n = size;
K = k_val;
tree.resize(4 * n + 1);
build(1, 1, n, arr);
}
void modify(int l, int r, int64_t v)
{
updateInternal(1, 1, n, l, r, v);
}
int64_t query(int l, int r)
{
Node ans_node = queryInternal(1, 1, n, l, r);
return add_k(add_k(ans_node.s1, ans_node.s2), ans_node.s4);
}
};
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int64_t n;
int64_t m;
int64_t K;
cin >> n >> m >> K;
vector<int64_t> arr(n + 1);
for (int i = 1; i <= n; ++i) {
cin >> arr[i];
}
KarySegmentTree KSTree(n, K, arr);
int t;
while (m--)
{
cin >> t;
if (t == 1) {
int64_t l, r, v;
cin >> l >> r >> v;
KSTree.modify(l, r, v);
} else if (t == 2) {
int l, r;
cin >> l >> r;
int64_t res = KSTree.query(l ,r);
cout << res << "\n";
}
}
return 0;
}
|
