/+ dub.sdl: name "A" dependency "dcomp" version=">=0.9.0" +/ import std.stdio, std.algorithm, std.range, std.conv; // import dcomp.foundation, dcomp.scanner; import std.container.rbtree; // import dcomp.modint; alias Mint = ModInt!(10^^9 + 7); Mint C(int n, int k) { if (k < 0 || n < k) return Mint(0); return fact[n] * iFac[k] * iFac[n-k]; } Mint superNaive(int[] v) { int n = v.length.to!int; int[] w; foreach (d; 1..n+1) { foreach (l; 0..n-d+1) { int r = l+d; w ~= v[l..r].reduce!((a, b) => max(a, b)); } } writeln(v); writeln(w); int m = w.length.to!int; Mint sm = 0; foreach (l; 0..m) { foreach (r; l+1..m+1) { sm += Mint(w[l..r].reduce!((a, b) => max(a, b))); } } return sm; } Mint i2 = Mint(1) / Mint(2); Mint solve(int a, int b) { if (a > b) swap(a, b); Mint ans = 0; ans += Mint(a) * Mint(a+1) * Mint(b) * i2; ans += Mint(a) * Mint(b) * Mint(b+1) * i2; ans -= Mint(a) * Mint(b); /* foreach (i; 1..a+1) { foreach (j; 1..b+1) { ans += Mint(i+j); } }*/ return ans; } Mint solve2(int a, int b) { b--; if (a > b) swap(a, b); Mint ans = 0; // foreach (i; 1..a+1) { // ans += Mint(i) * (Mint(a-i) + Mint(b-i) + Mint(1)); // ans -= Mint(i) * Mint(2 * i); // } ans -= Mint(a) * Mint(a+1) * Mint(2*a + 1) / Mint(3); ans += Mint(a) * Mint(a+1) * i2 * (Mint(a) + Mint(b) + Mint(1)); /* foreach (i; 1..a+1) { foreach (j; 1..b+1) { ans += Mint(min(i, j)); } }*/ return ans; } Mint calc(int[] v) { int n = v.length.to!int; int[] idx = iota(n).array; idx.sort!((a, b) => v[a] > v[b]); // writeln(idx); Mint all, csm; auto tr = new RedBlackTree!int(); tr.insert(-1); tr.insert(n); tr.insert(idx[0]); foreach (i; idx[1..$]) { Mint cnt; int l = tr.lowerBound(i).back; int r = tr.upperBound(i).front; // writeln(i, " : ", v[i], " start : ", l, " ", i, " ", r); // writeln("solve ", i-l, " ", r-i, " ", solve(i-l, r-i)); cnt += solve(i-l, r-i); tr.insert(i); if (l == -1) { int nl = tr.lowerBound(n).back; auto u = solve2(n-nl-1, r) - solve2(n-nl-1, i); // writeln("solveL ", n-nl-1, " (", r, " -> ", i, ") ", u); cnt += u; } if (r == n) { int nr = tr.upperBound(-1).front; auto u = solve2(n-l-1, nr) - solve2(n-i-1, nr); // writeln("solveR (", n-l-1, " -> ", n-i-1, ") ", nr, " ", u); cnt += u; } csm += cnt; all += cnt * Mint(v[i]); // writeln("end ", i, " ", cnt); // writeln(all); } Mint sa = Mint(n) * Mint(n+1) / Mint(2); Mint fc = sa * (sa+Mint(1)) / Mint(2) - csm; // writeln("first count", fc); all += fc * Mint(v[idx[0]]); // writeln("all ", all); return all; } void check() { import std.random; while (true) { int n = uniform(1, 10); int[] v = new int[n]; v.each!((ref x) => x = uniform(1, 10)); Mint a = calc(v); Mint b = superNaive(v); if (a != b) { writeln("ERROR!"); writeln(v, " ", a, " ", b); break; } } } int main() { int n; int[] v; sc.read(n, v); writeln(calc(v)); // writeln(superNaive(v)); // check(); return 0; } Scanner sc; static this() { sc = new Scanner(stdin); } Mint[] fact, iFac; static this() { // fact = factTable!Mint(1_100_000); // iFac = invFactTable!Mint(1_100_000); } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/modint.d */ // module dcomp.modint; // import dcomp.numeric.primitive; struct ModInt(uint MD) if (MD < int.max) { import std.conv : to; uint v; this(int v) {this(long(v));} this(long v) {this.v = (v%MD+MD)%MD;} static auto normS(uint x) {return (x a[n-1]*T(n)).take(length).array; } T[] invFactTable(T)(size_t length) if (isModInt!T) { import std.algorithm : map, reduce; import std.range : take, recurrence, iota; import std.array : array; auto res = new T[length]; res[$-1] = T(1) / iota(1, length).map!T.reduce!"a*b"; foreach_reverse (i, v; res[0..$-1]) { res[i] = res[i+1] * T(i+1); } return res; } T[] invTable(T)(size_t length) if (isModInt!T) { auto f = factTable!T(length); auto invf = invFactTable!T(length); auto res = new T[length]; foreach (i; 1..length) { res[i] = invf[i] * f[i-1]; } return res; } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/numeric/primitive.d */ // module dcomp.numeric.primitive; import std.traits; import std.bigint; Unqual!T pow(T, U)(T x, U n) if (!isFloatingPoint!T && (isIntegral!U || is(U == BigInt))) { return pow(x, n, T(1)); } Unqual!T pow(T, U, V)(T x, U n, V e) if ((isIntegral!U || is(U == BigInt)) && is(Unqual!T == Unqual!V)) { Unqual!T b = x, v = e; Unqual!U m = n; while (m) { if (m & 1) v *= b; b *= b; m /= 2; } return v; } T powMod(T, U, V)(T x, U n, V md) if (isIntegral!U || is(U == BigInt)) { T r = T(1); while (n) { if (n & 1) r = (r*x)%md; x = (x*x)%md; n >>= 1; } return r % md; } // import dcomp.int128; ulong ulongPowMod(U)(ulong x, U n, ulong md) if (isIntegral!U || is(U == BigInt)) { x %= md; ulong r = 1; while (n) { if (n & 1) { r = mul128(r, x).mod128(md); } x = mul128(x, x).mod128(md); n >>= 1; } return r % md; } T lcm(T)(in T a, in T b) { import std.numeric : gcd; return a / gcd(a,b) * b; } T[3] extGcd(T)(in T a, in T b) if (!isIntegral!T || isSigned!T) { if (b==0) { return [T(1), T(0), a]; } else { auto e = extGcd(b, a%b); return [e[1], e[0]-a/b*e[1], e[2]]; } } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/scanner.d */ // module dcomp.scanner; // import dcomp.container.stackpayload; class Scanner { import std.stdio : File; import std.conv : to; import std.range : front, popFront, array, ElementType; import std.array : split; import std.traits : isSomeChar, isStaticArray, isArray; import std.algorithm : map; File f; this(File f) { this.f = f; } char[512] lineBuf; char[] line; private bool succW() { import std.range.primitives : empty, front, popFront; import std.ascii : isWhite; while (!line.empty && line.front.isWhite) { line.popFront; } return !line.empty; } private bool succ() { import std.range.primitives : empty, front, popFront; import std.ascii : isWhite; while (true) { while (!line.empty && line.front.isWhite) { line.popFront; } if (!line.empty) break; line = lineBuf[]; f.readln(line); if (!line.length) return false; } return true; } private bool readSingle(T)(ref T x) { import std.algorithm : findSplitBefore; import std.string : strip; import std.conv : parse; if (!succ()) return false; static if (isArray!T) { alias E = ElementType!T; static if (isSomeChar!E) { auto r = line.findSplitBefore(" "); x = r[0].strip.dup; line = r[1]; } else static if (isStaticArray!T) { foreach (i; 0..T.length) { bool f = succW(); assert(f); x[i] = line.parse!E; } } else { StackPayload!E buf; while (succW()) { buf ~= line.parse!E; } x = buf.data; } } else { x = line.parse!T; } return true; } int read(T, Args...)(ref T x, auto ref Args args) { if (!readSingle(x)) return 0; static if (args.length == 0) { return 1; } else { return 1 + read(args); } } } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/foundation.d */ // module dcomp.foundation; static if (__VERSION__ <= 2070) { /* Copied by https://github.com/dlang/phobos/blob/master/std/algorithm/iteration.d Copyright: Andrei Alexandrescu 2008-. License: $(HTTP boost.org/LICENSE_1_0.txt, Boost License 1.0). */ template fold(fun...) if (fun.length >= 1) { auto fold(R, S...)(R r, S seed) { import std.algorithm : reduce; static if (S.length < 2) { return reduce!fun(seed, r); } else { import std.typecons : tuple; return reduce!fun(tuple(seed), r); } } } } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/container/stackpayload.d */ // module dcomp.container.stackpayload; struct StackPayload(T, size_t MINCAP = 4) if (MINCAP >= 1) { import core.exception : RangeError; private T* _data; private uint len, cap; @property bool empty() const { return len == 0; } @property size_t length() const { return len; } alias opDollar = length; inout(T)[] data() inout { return (_data) ? _data[0..len] : null; } ref inout(T) opIndex(size_t i) inout { version(assert) if (len <= i) throw new RangeError(); return _data[i]; } ref inout(T) front() inout { return this[0]; } ref inout(T) back() inout { return this[$-1]; } void reserve(size_t newCap) { import core.memory : GC; import core.stdc.string : memcpy; import std.conv : to; if (newCap <= cap) return; void* newData = GC.malloc(newCap * T.sizeof); cap = newCap.to!uint; if (len) memcpy(newData, _data, len * T.sizeof); _data = cast(T*)(newData); } void free() { import core.memory : GC; GC.free(_data); } void clear() { len = 0; } void insertBack(T item) { import std.algorithm : max; if (len == cap) reserve(max(cap * 2, MINCAP)); _data[len++] = item; } alias opOpAssign(string op : "~") = insertBack; void removeBack() { assert(!empty, "StackPayload.removeBack: Stack is empty"); len--; } } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/ldc/inline.d */ // module dcomp.ldc.inline; version(LDC) { pragma(LDC_inline_ir) R inlineIR(string s, R, P...)(P); } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/int128.d */ // module dcomp.int128; version(LDC) { // import dcomp.ldc.inline; } version(LDC) version(X86_64) { version = LDC_IR; } ulong[2] mul128(ulong a, ulong b) { ulong[2] res; version(LDC_IR) { ulong upper, lower; inlineIR!(` %r0 = zext i64 %0 to i128 %r1 = zext i64 %1 to i128 %r2 = mul i128 %r1, %r0 %r3 = trunc i128 %r2 to i64 %r4 = lshr i128 %r2, 64 %r5 = trunc i128 %r4 to i64 store i64 %r3, i64* %2 store i64 %r5, i64* %3`, void)(a, b, &lower, &upper); return [lower, upper]; } else version(D_InlineAsm_X86_64) { ulong upper, lower; asm { mov RAX, a; mul b; mov lower, RAX; mov upper, RDX; } return [lower, upper]; } else { ulong B = 2UL^^32; ulong[2] a2 = [a % B, a / B]; ulong[2] b2 = [b % B, b / B]; ulong[4] c; foreach (i; 0..2) { foreach (j; 0..2) { c[i+j] += a2[i] * b2[j] % B; c[i+j+1] += a2[i] * b2[j] / B; } } foreach (i; 0..3) { c[i+1] += c[i] / B; c[i] %= B; } return [c[0] + c[1] * B, c[2] + c[3] * B]; } } ulong div128(ulong[2] a, ulong b) { version(LDC_IR) { return inlineIR!(` %r0 = zext i64 %0 to i128 %r1 = zext i64 %1 to i128 %r2 = shl i128 %r1, 64 %r3 = add i128 %r0, %r2 %r4 = zext i64 %2 to i128 %r5 = udiv i128 %r3, %r4 %r6 = trunc i128 %r5 to i64 ret i64 %r6`,ulong)(a[0], a[1], b); } else version(D_InlineAsm_X86_64) { ulong upper = a[1], lower = a[0]; ulong res; asm { mov RDX, upper; mov RAX, lower; div b; mov res, RAX; } return res; } else { if (b == 1) return a[0]; while (!(b & (1UL << 63))) { a[1] <<= 1; if (a[0] & (1UL << 63)) a[1] |= 1; a[0] <<= 1; b <<= 1; } ulong ans = 0; foreach (i; 0..64) { bool up = (a[1] & (1UL << 63)) != 0; a[1] <<= 1; if (a[0] & (1UL << 63)) a[1] |= 1; a[0] <<= 1; ans <<= 1; if (up || b <= a[1]) { a[1] -= b; ans++; } } return ans; } } ulong mod128(ulong[2] a, ulong b) { version(D_InlineAsm_X86_64) { ulong upper = a[1], lower = a[0]; ulong res; asm { mov RDX, upper; mov RAX, lower; div b; mov res, RDX; } return res; } else { return a[0] - div128(a, b) * b; } } /* This source code generated by dcomp and include dcomp's source code. dcomp's Copyright: Copyright (c) 2016- Kohei Morita. (https://github.com/yosupo06/dcomp) dcomp's License: MIT License(https://github.com/yosupo06/dcomp/blob/master/LICENSE.txt) */