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poi08_per.cpp
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poi08_per.cpp
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#include <bits/stdc++.h>
using namespace std;
typedef long long lint;
typedef pair<int, int> pi;
const int MAXN = 300005;
static char buf[1 << 19]; // size : any number geq than 1024
static int idx = 0;
static int bytes = 0;
static inline int _read() {
if (!bytes || idx == bytes) {
bytes = (int)fread(buf, sizeof(buf[0]), sizeof(buf), stdin);
idx = 0;
}
return buf[idx++];
}
static inline int _readInt() {
int x = 0, s = 1;
int c = _read();
while (c <= 32) c = _read();
if (c == '-') s = -1, c = _read();
while (c > 32) x = 10 * x + (c - '0'), c = _read();
if (s < 0) x = -x;
return x;
}
int n, m;
struct bit{
int tree[MAXN];
void add(int x, int v){
while(x < MAXN){
tree[x] += v;
x += x & -x;
}
}
int query(int x){
lint ret = 0;
while(x){
ret += tree[x];
x -= x & -x;
}
return ret;
}
}bit;
int ipow(int x, int p){
if(p == 0) return 1;
if(p == 1) return x;
if(p & 1) return 1ll * ipow(1ll * x * x % m, p / 2) * x % m;
return ipow(1ll * x * x % m, p / 2);
}
struct seg{
int cnt[MAXN];
int tree[1050000], lim = (1<<19);
void init(){
fill(tree, tree + 1050000, 1);
}
void add(int x, int v){
cnt[x] += v;
if(v == 0) return;
if(v > 0) tree[x + lim] = 1ll * tree[x + lim] * ipow(x, v) % m;
else tree[x + lim] = ipow(x, cnt[x]);
x += lim;
while(x > 1){
x >>= 1;
tree[x] = 1ll * tree[2*x] * tree[2*x+1] % m;
}
}
}seg;
int a[MAXN];
int che[MAXN];
int occ[MAXN];
int cut[MAXN];
vector<int> cnd;
void constantcut(){
for(auto &i : cnd){
if(cut[i]) seg.add(i, cut[i]);
cut[i] = 0;
}
cnd.clear();
}
void add_num(int x, int v){
while(x != 1){
int cnt = 0, cv = che[x];
while(che[x] == cv) x /= cv, cnt++;
cut[cv] += v * cnt;
cnd.push_back(cv);
}
}
int main(){
n = _readInt();
m = _readInt();
for(int i=2; i<MAXN; i++){
for(int j=i; j<MAXN; j+=i){
if(!che[j]) che[j] = i;
}
}
for(int i=1; i<=n; i++){
a[i] = _readInt();
occ[a[i]]++;
}
for(int i=1; i<=n; i++) add_num(i, 1);
for(int i=1; i<MAXN; i++){
for(int j=1; j<=occ[i]; j++){
add_num(j, -1);
}
}
seg.init();
for(int i=1; i<MAXN; i++){
if(occ[i]) bit.add(i, occ[i]);
}
constantcut();
lint ans = 1;
for(int i=1; i<=n; i++){
int occSum = bit.query(a[i] - 1);
if(occSum != 0){
add_num(occSum, 1);
add_num(n - i + 1, -1);
constantcut();
ans += seg.tree[1];
add_num(occ[a[i]], 1);
add_num(occSum, -1);
}
else{
add_num(occ[a[i]], 1);
add_num(n - i + 1, -1);
}
occ[a[i]]--;
bit.add(a[i], -1);
}
ans %= m;
cout << ans << endl;
}